Tarea 2 modelacion estadisticas
OCTAVIO HERNANDEZ SATURNINO
2023-10-07
#tinytex::install_tinytex()
library(tinytex)¿Para qué sirve la generación de números (pseudo) aleatorios?
producen sucesiones que poseen una distribución uniforme según varios tipos de pruebas. Las clases más comunes de estos algoritmos son generadores lineales congruentes, generadores Fibonacci demorados, desplazamiento de registros con retroalimentación lineal y desplazamientos de registros con retroalimentación generalizada.
¿Cuáles son las principales características que acompañan a los números aleatorios puros?
se almacenaban en tablas de dígitos aleatorios. su procedimiento son: números aleatorios en un rango de \(1\) a \(m\) era el siguiente:
Se selecciona al azar un punto de inicio en la tabla y la dirección que se seguirá.
Se agrupan los dígitos de forma que \(“cubran”\) el valor de \(m\).
Se va avanzado en la dirección elegida, seleccionando los valores menores o iguales que m y descartando el resto.
Mencione tres funciones que existan en el software R para generar números pseudoaleatorios, y de un ejemplo de cada una de ellas.
\(Números\)_\(pseudoaleatorios\). Los números pseudoaleatorios se generan de manera secuencial con un algoritmo determinístico, formalmente se definen por:
\(Función\) de \(inicialización.\)Recibe un número (la semilla) y pone al generador en su estado inicial.
\(ejemplo\)
Se inicia con una semilla de$ 4 $ dígitos. \(seed = 9731\)
\(Función de transición\). Transforma el estado del generador.
\(ejemplo\) La semilla se eleva al cuadrado, produciendo un número de 8 dígitos (si el resultado tiene menos de 8 dígitos se añaden ceros al inicio). \(value = 94692361\)
\(Funció\)n de \(salidas\). Transforma el estado para producir un número fijo de bits (0 ó 1).
Una sucesión de \(bits\) pseudoaleatorios se obtiene definiendo la semilla y llamando repetidamente la función de transición y la función de salidas.
\(Ejemplo\) Los \(4\) números del centro serán el siguiente número en la secuencia, y se devuelven como resultado. \(seed = 6923\)
CODIGO.
library(tidyverse)
mid_square <- function(seed, n) {
seeds <- numeric(n)
values <- numeric(n)
for(i in 1:n) {
x <- seed ^ 2
seed = case_when(
nchar(x) > 2 ~ (x %/% 1e2) %% 1e4,
TRUE ~ 0)
values[i] <- x
seeds[i] <- seed
}
cbind(seeds, values)
}
x <- mid_square(1931, 10)
print(x, digits = 4)## seeds values
## [1,] 7287 3728761
## [2,] 1003 53100369
## [3,] 60 1006009
## [4,] 36 3600
## [5,] 12 1296
## [6,] 1 144
## [7,] 0 1
## [8,] 0 0
## [9,] 0 0
## [10,] 0 0Por otra parte esta funcion permite \(runif\) para generar las variables aleatorios provienen de la distribucion uniforme.asi se define\[ks.test(datos,runif,0,1)\]
tambien la funcion \(rnorm\) para generar las variables aleatorios provienen de la distribucion normal .asi se define\[ks.test(datos,rnorm,0,1)\]
¿Cualés son las principales características de los generadores congruenciales?
En los generadores congruenciales lineales se considera una combinación lineal de los últimos \(K\) enteros generados y se calcula su resto al dividir por un entero fijo \(m\) En el método congruencial simple (de orden \(k=1\), partiendo de una semilla inicial,el algoritmo secuencial es el siguiente:
\[\begin{aligned} x_{i} & = (ax_{i-1}+c) \bmod m \\ u_{i} & = \dfrac{x_{i}}{m} \\ i & =1,2,\ldots \end{aligned}\]
\(a\)(multiplicador),\(c\) (incremento) y \(m\) (módulo) son enteros positivos6 fijados de antemano (los parámetros de este generador). Si el generador se denomina congruencial multiplicativo (Lehmer, 1951) y en caso contrario se dice que es mixto (Rotenburg, 1960).
Obviamente los parámetros y la semilla determinan los valores generados, que también se pueden obtener de forma no recursiva:\[x_{i}=\left( a^{i}x_0+c\frac{a^{i}-1}{a-1}\right) \bmod m\]
Este método está implementado7 en la función \(rlcg()\) del paquete simres, imitando el funcionamiento del generador uniforme de R (ver también simres::rng(); fichero rng.R
Méncione almenos 3 tipos diferentes de generadores congruenciales.
Ejemplos de parámetros:
1-\[c=0,a=2^{16} +3=65539 y m=2^{31}\] generador RANDU de IBM (no recomendable como veremos más adelante).
2-\[c=0,a=7^5=16807 y m=2^{31}-1\] (primo de Mersenne), Park y Miller (1988) minimal standar, empleado por las librerías IMSL y NAG.
3-\[ c=0,a=4871 y m=2^31-1\] actualización del minimal standar propuesta por Park, Miller y Stockmeyer (1993).
una adecuada elección de los parámetros permite obtener de manera eficiente secuencias de números “aparentemente” i.i.d.\(\mathcal{U}(0,1)\).Durante los primeros años, el procedimiento habitual consistía en escoger de forma que se pudiera realizar eficientemente la operación del módulo, aprovechando la arquitectura del ordenador (por ejemplo \(m=2^{31}\)si se emplean enteros con signo de 32 bits). Posteriormente se seleccionaban y de forma que el período \(p\) fuese lo más largo posible (o suficientemente largo)
Simulación
#SIMULACION
######################################################################3
#1.PASO 1 GENERAR LOS DATOS
rm(list=ls())
n <- 100 # numero de numeros aleatorios a generar (100)
a <- 2^16+3 #valor de operacion
m <- 2^31 #valor del modulo
c <- 0
muestr <-45183 # Fijar un valor a la semilla asignamos el valor de muestr
# Enseguida se utiliza el ciclo for para generar los valores aleatorios en n muestra
#iniciando en la posicion 2,tomara el valor de 2-1, pues en este caso la semilla inicial 45183, sera el primer posicion.
for(i in 2:n)
{
muestr[i]<-(a*muestr[i-1]+c)%%m
}
muestr## [1] 45183 813764989 587215991 494378341 1976293423 965904525
## [7] 893688231 963955957 2035508959 1389966493 757636567 626055557
## [13] 1232571535 1760929197 1619915015 313578261 187136319 448097213
## [19] 1004356407 1993263525 772889839 1730352845 1278624871 688508213
## [25] 1213360031 1083586269 2023728279 242609605 421972303 348347373
## [31] 439817159 1651260245 1654239743 1506547197 593576439 739952101
## [37] 1245008303 810480909 100261671 1897176437 1890768991 712476957
## [43] 142842711 887214597 1890219535 1208902189 978855559 1435464597
## [49] 1950571199 931729469 920137911 1430229541 300136047 1813652301
## [55] 1738238439 549010869 534821151 415312733 1973453335 1660454469
## [61] 791581391 542816365 427632967 1975417813 1561359231 179329661
## [67] 2056130423 2132880997 734563119 243835277 1294394535 1276882421
## [73] 306711007 1085742493 1606572247 2015234693 1927225231 2016173741
## [79] 1194466311 1906136085 686619711 1996879037 1506729527 1805884069
## [85] 1569705967 1755213773 698896231 1281355317 1398065823 1151164381
## [91] 766844823 683040453 1491606607 654791917 1241710279 1557134421
## [97] 314897663 760078077 1726389495 1370150629#A aprtir de la Asignacion de la mestr
#podemos calcular
#los siguientes
########################################################
#2.Calcular la media y varianza de la muestra.
##############################################
# 1 generar la media de la muestr a partir de la muestra generada
mean(muestr)## [1] 1135632983# 1 Genrar la varianza de la muestr a partir de la muestra generada
var(muestr)## [1] 3.564065e+17#las funciones de ggplot unicamente trabaja con data frame
## guardar en los resultados de muestr/m como dataframe
## en datos
v <- muestr/m
dat <- data.frame(v)
###################################################
#3.Generar el histograma de la muestra con ggplot.
##############################################
library(ggplot2)
## generando graficos ...
ggplot(dat, aes(v))+geom_histogram(binwidth = 0.1,col="black",fill="orange",alpha=0.4,) + labs(y="Conteo",x="Valor de datos muestr/m",title = "Valores generados con operador congrencial multiplicativo")+ theme_bw()
###################################################
#4.Verificar que la muestra provengan de una distribución uniforme
###########################################################
ks.test(v,punif,0,1)##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: v
## D = 0.073395, p-value = 0.6542
## alternative hypothesis: two-sided####################################################3
#5.probar independencia en la muestra. Discutir los resultados.
###############################################3########
prueIND<- acf(v, type= "correlation");prueIND # Ver si hay independencia en la muestra generada
##
## Autocorrelations of series 'v', by lag
##
## 0 1 2 3 4 5 6 7 8 9 10
## 1.000 0.104 -0.243 -0.069 0.099 0.086 -0.077 0.061 0.048 -0.043 0.010
## 11 12 13 14 15 16 17 18 19 20
## -0.038 -0.019 0.117 0.046 0.020 -0.136 -0.019 0.132 0.020 -0.051Box.test(v, lag = 10, type = "Ljung")##
## Box-Ljung test
##
## data: v
## X-squared = 11.133, df = 10, p-value = 0.3473Para cada uno de los sigueintes generadores: Generar$ 1000$ valores; generar el histograma de la muestra con$ ggplot$; calcular la media y varianza de la muestra; y verificar que la muestra provengan de una distribución uniforme, además de probar independencia en la muestra. Discutir los resultados.
\(c=0\), \(a=2^{16}+3\) y \(m=2^{31}\)
rm(list=ls())
n <- 1000 # numero de numeros aleatorios a generar (1000)
a <- 2^16+3 #valor de operacion
m <- 2^31 #valor del modulo
c <- 0
muestr <-45183 # Fijar un valor a la semilla asignamos el valor de muestr
# Enseguida se utiliza el ciclo for para generar los valores aleatorios en n muestra
#iniciando en la posicion 2,tomara el valor de 2-1, pues en este caso la semilla inicial 45183, sera el primer posicion.
for(i in 2:n)
{
muestr[i]<-(a*muestr[i-1]+c)%%m
}
muestr## [1] 45183 813764989 587215991 494378341 1976293423 965904525
## [7] 893688231 963955957 2035508959 1389966493 757636567 626055557
## [13] 1232571535 1760929197 1619915015 313578261 187136319 448097213
## [19] 1004356407 1993263525 772889839 1730352845 1278624871 688508213
## [25] 1213360031 1083586269 2023728279 242609605 421972303 348347373
## [31] 439817159 1651260245 1654239743 1506547197 593576439 739952101
## [37] 1245008303 810480909 100261671 1897176437 1890768991 712476957
## [43] 142842711 887214597 1890219535 1208902189 978855559 1435464597
## [49] 1950571199 931729469 920137911 1430229541 300136047 1813652301
## [55] 1738238439 549010869 534821151 415312733 1973453335 1660454469
## [61] 791581391 542816365 427632967 1975417813 1561359231 179329661
## [67] 2056130423 2132880997 734563119 243835277 1294394535 1276882421
## [73] 306711007 1085742493 1606572247 2015234693 1927225231 2016173741
## [79] 1194466311 1906136085 686619711 1996879037 1506729527 1805884069
## [85] 1569705967 1755213773 698896231 1281355317 1398065823 1151164381
## [91] 766844823 683040453 1491606607 654791917 1241710279 1557134421
## [97] 314897663 760078077 1726389495 1370150629 1273332911 1751092749
## [103] 1194043943 2141847157 2104687455 1941434909 1296356951 1042645765
## [109] 1031112975 1097833261 1601950087 1878684821 1149525439 726407485
## [115] 455166903 488301349 980789615 1490025549 113046759 152952501
## [121] 2047777823 172676189 1933409559 1456437061 2075354575 1491677549
## [127] 1009292359 1220590805 387397247 2076484477 382397047 785891173
## [133] 1273773615 569621133 543698855 283086581 1100197087 1905919645
## [139] 1533744087 639122309 768455311 1006114733 1268074247 700896533
## [145] 1382645567 1987804605 1630501175 482700197 1106592495 147769549
## [151] 1664703079 68357941 460205471 2146011357 144284311 878956485
## [157] 1827696463 908086765 1884154311 984661333 1835481087 3450877
## [163] 681244663 1908926437 1027389359 1868900109 1966896423 1423728501
## [169] 1577721439 947739421 76878167 521548805 289905679 1340462125
## [175] 1138654343 1210217877 1308385471 1253319229 39413431 1841509413
## [181] 2104401007 347788621 326991847 979337141 785612575 194608477
## [187] 539588631 1486055493 1912551631 248293997 1456668487 62914005
## [193] 152369535 347991165 716621175 1167806565 557248815 1423168397
## [199] 1376287399 1891659765 1110855647 377614237 857919191 1748987013
## [205] 625165711 895013037 1891070471 1143821845 580715071 1779828413
## [211] 1157567543 1664367781 1715582447 1756635597 1542022503 2032349237
## [217] 463376543 1668985309 1548555671 712917189 1077920335 51267309
## [223] 1343739079 1158577749 1300265727 1669361917 461263607 628226277
## [229] 1765468847 643809293 858538023 1504428149 1299726687 700957725
## [235] 1098140759 280225029 388017935 1953565997 1786783623 1728542357
## [241] 732652479 1723935549 1602257335 540575013 1708035951 1088073293
## [247] 1893534439 1568546997 959406623 229451357 1331983127 1631869253
## [253] 2098334671 50668397 746351175 1874607829 235519103 1721513341
## [259] 1766957175 1550573925 1990763567 136899725 84395431 1421758709
## [265] 1328542431 1617877149 2045348311 2006162821 71293071 1699645869
## [271] 966302983 1238423317 881296703 584421309 2017308471 401608101
## [277] 1433741551 693009101 1991798887 1418744117 1323692959 1615911645
## [283] 2077200535 67482053 1037440335 1322336237 744538055 1156136789
## [289] 235978239 1748056573 1922084343 94964197 450895279 1850693901
## [295] 603654951 1998070133 113075295 2023173405 383944535 1274975749
## [301] 2046870031 806438445 1449185927 1437169557 2022794943 1349727293
## [307] 630627511 226154021 2123727471 2117044045 31167975 460964277
## [313] 337790239 25546589 1408134679 1776437829 132898511 1989319789
## [319] 2413895 1437958101 16088959 39812733 94075767 206140005
## [325] 390158127 485688717 1550192807 634991093 595629535 6341021
## [331] 1119831255 219467397 1975741327 1289306797 691587079 1135695893
## [337] 589891647 1908021437 1844136503 335077029 445619183 1805505485
## [343] 380009319 1062892085 809784991 1735132125 975244183 972694213
## [349] 1353934927 1516845293 1210624711 54591573 169345279 524747517
## [355] 1624377591 728570597 489443503 674492941 1789449767 371294837
## [361] 1155106655 1441502749 400540247 167134981 1692914959 63340333
## [367] 176192903 487094421 1336830399 1489648957 1201387447 243935013
## [373] 1388541295 1840865357 695804135 491938485 984360991 1478719581
## [379] 13068567 1802320709 2106372559 712316269 348930119 2125185237
## [385] 1020805759 2030552957 848582263 1848902501 1308690991 1949441677
## [391] 2065914791 1292964597 2049456351 660056733 547618775 1640169349
## [397] 617479823 1828256685 1117254407 986634517 159484735 667132349
## [403] 419947831 810463141 1083248367 1352805581 515081831 1652658997
## [409] 985250207 1774988509 1782679191 1163629509 1675082575 1725313517
## [415] 1718588871 1226162517 479609855 432131069 423781367 800992229
## [421] 991921071 890080013 708157735 533193589 1120709215 1925512989
## [427] 1466694999 60487685 47573007 1888532525 165619847 1176795541
## [433] 1275227327 1355171389 948949687 2087090213 1834510447 813185357
## [439] 1253420007 201851829 667749151 42344797 686777367 1592077381
## [445] 1223984335 1605144173 762489671 866058709 481428863 1536495741
## [451] 591147383 455840869 1709686063 1860581261 71280295 862319605
## [457] 237427679 106140573 647477975 782119045 1012896143 1185789101
## [463] 146152967 942234133 43060799 368192189 1821605943 1173455013
## [469] 1383694831 2036041165 1910477159 1728427061 1766202527 1483822557
## [475] 1597047191 522847429 1648561743 890776301 1245020359 1600619093
## [481] 546014975 1755419901 1323417335 731659493 1069135535 1977361421
## [487] 94465063 2097890421 999738719 2320413 1753692247 1911335173
## [493] 2127231759 2003824941 1467798407 1509784213 143486911 157765437
## [499] 1802694071 806340901 1498700655 1735135821 1217476327 278570165
## [505] 1451552287 1907214941 526802711 1028267333 1428379599 1463355245
## [511] 219682375 1032798933 2072168575 990337405 177409143 741352805
## [517] 703950895 1846497421 448459175 1104663797 444366559 1314159773
## [523] 1738175959 749101445 1735926927 1526164909 2123581703 1153489685
## [529] 693604671 222671805 1536039735 769741221 1531507951 113893069
## [535] 1932172391 1978062133 921272223 609976029 1810857111 1080391109
## [541] 922050895 103752685 913992647 255214421 1895287295 484859389
## [547] 883956215 940002789 1979378095 1268759821 535574311 384542069
## [553] 1782050911 788975901 1580299095 233527813 63376911 425994797
## [559] 1985576583 1637055381 542077631 1403869245 1397033143 42342949
## [565] 565661295 865397581 101433831 1409959349 1104400671 379220829
## [571] 925653527 2140933701 219753167 1377468525 1992065351 1702659029
## [577] 877300607 677290621 463005559 977385061 1697260335 1387096461
## [583] 1637170343 1634121205 1512645087 811230621 1990996183 349934213
## [589] 1360508815 718677677 657421319 1771396117 416617535 1589525693
## [595] 1492629047 1092493989 1711237103 434976717 93628263 941946421
## [601] 514056863 1049274333 1669134231 571336389 1290712143 454761709
## [607] 1849579207 562168917 1759186175 1200629501 2108519671 1845452517
## [613] 685972655 391665165 471204391 1449723509 162534239 812595741
## [619] 1265282647 278334213 1019879695 1466786605 1769286023 1709603989
## [625] 776500671 9986365 1661346743 1288268581 1367425391 905102413
## [631] 1713720551 2136401589 1689891871 1649155165 1128355095 517668677
## [637] 1540750799 290519405 761261127 1952892117 571035263 882568061
## [643] 156090999 1583368037 1652938287 2109768333 2077132711 2064815861
## [649] 137151711 1566920349 1724705751 540918661 608062095 927588269
## [655] 92970759 799464725 1812567871 1532741053 1473270071 1487401893
## [661] 2107431663 1405456589 203272807 1455429429 460670367 402575581
## [667] 416903831 1025726405 254740303 886838765 880886215 1598735701
## [673] 1664438271 2040459261 1557778423 1719955429 594694063 973467405
## [679] 488557863 612591477 1426011743 895263517 1127410007 854572037
## [685] 1423193103 848010285 869258375 1878424981 1299740863 1630038589
## [691] 230047415 1742322725 1941058671 260414797 1272829927 998279093
## [697] 976656159 1170392413 379932695 335999045 744083663 1440510573
## [703] 1946310471 860751317 532615551 1891382397 112303479 831248485
## [709] 1829275951 1346935693 208065191 2010871797 1602709471 108345245
## [715] 1258071767 130872453 200007055 22190253 480561671 536174101
## [721] 1039473215 1411272381 1259858999 1300153509 757157359 1431497165
## [727] 1774566759 2058893365 677226655 565705181 1594158487 178636997
## [733] 1756781135 343019245 1279470791 294684245 990286591 1142077693
## [739] 87370487 982941925 816349871 346589197 1174837287 1782237301
## [745] 119888223 1859062813 1485448279 771058949 1994737423 733926701
## [751] 1483308935 147029653 417299391 1180529469 1179998647 750193957
## [757] 323626863 1632466509 439706343 830941365 1028291103 838757981
## [763] 72895255 1478484293 1772397519 1622993773 228835911 1798457045
## [769] 141284479 1841462653 1187281015 1287940453 1337080879 725988493
## [775] 912137639 1086413045 456723167 1552556189 909861335 76096901
## [781] 857763983 166744493 1870525703 1132519189 697802047 436590525
## [787] 634292023 2023921061 2139930863 1066746573 26003559 1292720437
## [793] 1079839647 1287004893 150956183 60111301 1149545807 2061305837
## [799] 2021922759 22234965 1263457791 938181117 700417527 53842405
## [805] 461747631 138420493 969761575 277817717 1528986719 231109917
## [811] 510680919 984096261 1308449295 1141313069 1514285703 961380245
## [817] 729644735 20413501 2145612983 1952538149 994646639 1279938381
## [823] 875294183 174770613 1760910623 402593629 1599751703 1680200261
## [829] 2125887183 1928488045 1027878215 1695778773 923768703 1018021501
## [835] 2089177975 1225390693 1434644271 1874316685 481585319 1053047285
## [841] 1984015839 279185821 998841559 1332893317 1155269519 1378028205
## [847] 18227207 592011285 1240539199 2115133629 1525948983 856909477
## [853] 2145334255 864852941 913494887 1992260149 1584623263 167332829
## [859] 1774773143 552708805 228196431 689766637 2084831943 2006124629
## [865] 1863194879 1713982205 2105073911 1499570917 789178543 1976351245
## [871] 460533287 8424053 200712031 1128455709 669358679 302501637
## [877] 85749007 2086946605 1012520327 177504405 542278079 1656128829
## [883] 761302967 400076581 1991183727 1903962189 2093054183 1865116341
## [889] 943144991 1757724765 2058043671 823706437 1452231119 1300028781
## [895] 1172543559 1777453269 111827583 1853755261 1526148727 1063029605
## [901] 1232773679 2124342925 1651094439 1524898549 731992287 1405285021
## [907] 1843779543 562595717 1813943951 1525334957 1416448775 1213128981
## [913] 973185855 1363405245 1569242423 1439774629 957916911 1379464397
## [919] 1803017831 550411061 2107691423 1249998045 1415667351 1538988997
## [925] 787895119 1613887981 444788167 1028639061 21257215 1607209981
## [931] 862010359 1444590565 909450159 1045320461 234354983 588180341
## [937] 1419887199 1078216477 132765015 1830060037 1195540495 1440120877
## [943] 28344455 93880725 308184255 1004179005 1103932087 1880948773
## [949] 1350303855 1910702413 1458963431 147393461 638591775 357525853
## [955] 692796439 939045957 1546591439 828135021 1786905415 1120733653
## [961] 1379671423 338909309 353831287 1220287589 1989760303 955973517
## [967] 712900263 2116090869 1985475551 1457970077 1615958743 868989061
## [973] 1407723919 625441965 1820554759 999383573 348726847 1687843517
## [979] 546068535 970721445 909711855 1016745421 60549479 1950006325
## [985] 417674399 2135858653 466147735 754027717 328836687 1629221613
## [991] 373348551 461998677 1559338751 903077117 2121832183 308331749
## [997] 2080853679 1120201741 878429223 1631210613#A aprtir de la Asignacion de la mestr
#podemos calcular
#los siguientes
# 1 generar la media de la muestr a partir de la muestra generada
mean(muestr)## [1] 1094861823# 1 Genrar la varianza de la muestr a partir de la muestra generada
var(muestr)## [1] 3.862126e+17#las funciones de ggplot unicamente trabaja con data frame
## guardar en los resultados de muestr/m como dataframe
## en datos
v <- muestr/m
dat <- data.frame(v)
library(ggplot2)
## generando graficos ...
ggplot(dat, aes(v))+geom_histogram(binwidth = 0.1,col="black",fill="orange",alpha=0.4,) + labs(y="Conteo",x="Valor de datos muestr/m",title = "Valores generados con operador congrencial multiplicativo")+ theme_bw()
Probar que provenga de una distribucion uniforme [0,1] DECISION DE HIPOTESIS A PROVAR \[H_0: U\sim Uniforme(0,1)\] \[H_1: U\nsim Uniforme(0,1)\]
ks.test(v,punif,0,1)##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: v
## D = 0.02403, p-value = 0.6106
## alternative hypothesis: two-sidedDe acuerdo a los resultados, p-valor = 0.61, si alpha es mayor que p-valor se rechaza Ho. Note que p-valor es mayor que alpha Por lo tanto NO RECHAZA. es decir, la muestra simulada proviene de una distribución uniforme ########################################################################################### ##########################################################################################
Prueba de independencia de la muestra generada (autocorrelacion)
prueIND<- acf(v, type= "correlation");prueIND # Ver si hay independencia en la muestra generada
##
## Autocorrelations of series 'v', by lag
##
## 0 1 2 3 4 5 6 7 8 9 10
## 1.000 0.018 0.006 0.044 0.021 -0.014 -0.034 -0.011 0.016 -0.005 0.010
## 11 12 13 14 15 16 17 18 19 20 21
## 0.025 -0.048 0.067 -0.004 0.028 -0.008 -0.034 0.003 0.029 -0.011 0.014
## 22 23 24 25 26 27 28 29 30
## 0.062 0.013 0.042 -0.054 -0.013 0.048 0.016 -0.030 -0.027No hay correlación en los datos de la muestra generada de una uniforme Como en el gráfico se ve que las barras salen del rango, Por lo tanto se concluye , que la muesta es independiente.
Con el estadístico Ljung-Box, se puede probar \(H_{0}\): Muestra aleatoria \(H_{1}\): Muestra no aleatoria
Se rechaza \(H_{0}\) si \(p-valor <\alpha\)
Box.test(v, lag = 10, type = "Ljung")##
## Box-Ljung test
##
## data: v
## X-squared = 4.6693, df = 10, p-value = 0.9121De acuerdo a los resultados, p-valor = 0.9121, Note que \(p-valor > \alpha\), llegamos a conclusion ,que No se rechaza \(H0\) Por lo tanto La muestra generada es aleatoria
- \(c=0\), \(a=7^5\) y \(m=2^{31}-1\)
rm(list=ls())
n <- 1000 # numero de numeros aleatorios a generar (1000)
a <- 7^5 #valor de operacion
m <- 2^{31}-1 #valor del modulo
c <- 0
muestr1 <-45183 # Fijar un valor a la semilla asignamos el valor de muestr
# Enseguida se utiliza el ciclo for para generar los valores aleatorios en n muestra
#iniciando en la posicion 2,tomara el valor de 2-1, pues en este caso la semilla inicial 45183, sera el primer posicion.
for(i in 2:n)
{
muestr1[i]<-(a*muestr1[i-1]+c)%%m
}
muestr1## [1] 45183 759390681 583861446 1106539779 405682633 47433606
## [7] 500183005 1324770677 310316243 1394801185 492025643 1662940951
## [13] 1696381399 1089275421 153910072 1196269116 953129398 1165269213
## [19] 1776285898 1866910739 285224056 577209088 969508517 1571215430
## [25] 1958808498 770117376 478797963 536138832 43966612 212473316
## [31] 1921200698 56014994 846166772 888226570 1265131693 832775304
## [37] 1303606829 1091808309 1921969395 90603591 208648214 2057220794
## [43] 1223168058 2072081722 1882681902 1210672016 357017587 325274991
## [49] 1550892122 1834870815 808616785 1145787279 760935504 777897843
## [55] 248604365 1437869140 633156289 676278338 1726566842 1609875230
## [61] 1026522057 2020075648 1842440513 1330995898 1858390534 967542970
## [67] 748521706 445108616 1254966611 1786933890 439085935 963498453
## [73] 1491801191 831038412 28950396 1238001350 119633667 638347677
## [79] 2028590574 1071397446 326494827 577839304 824130594 2040853855
## [85] 1021931101 21805801 1417877417 1787200407 623469860 1085223307
## [91] 769506778 953895612 1158126029 1979876642 527611829 612031540
## [97] 2114907297 97615535 2094274084 1207555458 1664118456 11871464
## [103] 1955199924 250356274 817432645 1137574656 170334151 210374406
## [109] 1004558680 101302046 1776438698 140053045 229450203 1636415456
## [115] 411501863 1214468101 1880792419 1666385940 1614253053 1590149220
## [121] 203953625 464674763 1538201249 1140249357 26877271 754727827
## [127] 1672169207 29373760 1911029157 901617167 835112537 1930776214
## [133] 2077922528 1264860582 571180021 570710857 1275406097 1715991572
## [139] 2112455041 1832221883 1385173248 1884045656 508965377 753725238
## [145] 2001525060 1447836812 656095127 1809755791 1754686876 1776884328
## [151] 1187305514 625725874 347344959 966173367 1351924202 1413077754
## [157] 576159305 505674812 1283774105 623181326 530799663 502866403
## [163] 1327484276 820618049 987568509 162823100 673675422 929030570
## [169] 2010676300 633904908 373415989 1055310589 537628750 1462698321
## [175] 1325373838 1857708582 243393941 1913102499 1388537809 450163914
## [181] 320014217 1179893031 598175619 1166676926 1813398172 695158580
## [187] 1219214380 47124986 1755657606 912074262 493849148 98334781
## [193] 1297739724 1267622336 1890822912 597673678 1320489127 1364749391
## [199] 70180930 562368307 648605302 482318542 1724451616 419010200
## [205] 705552887 1970156722 373673561 1089355899 1506503818 977470996
## [211] 105130222 1692083320 1865905666 572831321 406822546 2026082221
## [217] 1863181515 2032665698 842529810 2038831999 1400335661 1168166954
## [223] 1086495004 668081787 1406087593 1204123963 1973040460 1596017893
## [229] 54492974 1035380396 578323931 379321995 1533305669 464614883
## [235] 531798089 103543009 785598193 819367995 1452747401 1583985864
## [241] 1843128036 1293077 257908669 1049000237 1853725036 2011413023
## [247] 131106487 188505187 668298584 754827478 1199519917 1902250630
## [253] 1537285521 781994390 379793090 861064746 22888889 293984610
## [259] 1786952170 746317895 2060362785 343519620 1098210204 2144436310
## [265] 323014569 67201567 2027821894 1037094568 1471125324 1224092557
## [271] 430267239 924046424 1993996711 1620410342 1996490387 581949934
## [277] 1192012300 275783237 819154033 4171714 1394520494 69419300
## [283] 646554779 378916833 1166198876 221262763 1469064784 952335129
## [289] 700892012 944241889 2116760740 1183660978 1649035085 2056209060
## [295] 1398823896 1529736363 604831057 1355473748 940755260 1499045606
## [301] 181353438 727937373 229091052 2042615540 565799838 340288350
## [307] 477346489 1911019078 732219414 1330393788 328662352 500209980
## [313] 1778139502 808178462 221343559 679519509 366353017 459540770
## [319] 1150526778 960800258 1240394413 1685137862 1097709998 179925009
## [325] 342651287 1536523002 851239439 245194959 2118040967 1225599697
## [331] 2138449102 627741122 2005363390 1534139712 1597473702 899954720
## [337] 811653219 639525989 357643888 114097663 2084008917 479585449
## [343] 886514152 401809778 1528352678 971557379 1646700712 1477107695
## [349] 838070545 106409142 1712055290 379872877 54561208 34705587
## [355] 1328732372 322531051 530649129 120325112 1522045557 194473435
## [361] 44911311 1057643880 1098544941 1327910128 1535461672 193335305
## [367] 243713224 836840939 915257570 308615529 728188398 153100933
## [373] 481971825 192146291 1734791396 253517253 256915523 1537064591
## [379] 1363791174 1145296987 1110532448 938477459 1870749845 384569188
## [385] 1676048893 810746952 440282049 1739233628 1899666479 1055132604
## [391] 1841202149 1992648620 437881375 45811356 1152314666 945062816
## [397] 881695300 1015742800 1241729597 503255233 1420099145 473077257
## [403] 1024997205 14208201 426549390 715184044 632255249 564884587
## [409] 2137533969 279486320 779844251 749628916 1874117910 1157062821
## [415] 1290408962 466073281 1420773158 1063795513 1409825716 1753731461
## [421] 751609952 809651610 1358221878 2031419583 1373911475 1585987781
## [427] 1129608703 1578031841 558111237 2114473810 1401934114 116079114
## [433] 1026517522 1943855903 717439910 2039373112 1904887264 754036572
## [439] 791664657 1846697034 2003383994 478685845 799255253 572825186
## [445] 303711601 2059732735 491687505 274822879 1858286303 1363216200
## [451] 71643557 1522420179 48294448 2083452617 1867269584 2021364677
## [457] 2032314446 1381488387 82128945 1656677241 1648906132 2036379636
## [463] 985660013 298985533 2085602798 1498139652 2134853736 329966876
## [469] 950508378 63459013 1403742579 446179311 2070268300 1469269406
## [475] 96449789 1828933885 1958365684 1917677066 963874086 1362614081
## [481] 689247759 660293595 1506447116 24480482 1274084397 977016142
## [487] 1050333632 641774684 1644238754 901168882 1890721130 1034507251
## [493] 935761445 1319859134 1513875275 315497269 425475640 1996020617
## [499] 1276460132 103804994 893812794 663517993 2011813127 413203474
## [505] 1896156767 49461489 223074234 1849686823 713160189 977062616
## [511] 1831422150 828962599 1647983304 1558794969 1514034230 839570307
## [517] 1690588959 372500456 700332987 138643302 158219719 614062247
## [523] 1885261494 1616201820 2130821484 1279384216 2004244548 2057115041
## [529] 1593261034 964603995 745292762 2010821630 928982571 1203957107
## [535] 1316175315 1876955105 1597158952 2052402411 1844983563 1122364308
## [541] 80569308 1213661946 1216647216 1997956225 1595969083 1381626951
## [547] 263490446 372645808 995780404 741188957 1757647699 2147312608
## [553] 1420314821 1950460142 45735139 2018819194 52570958 944312189
## [559] 1150809193 1412381869 1765321992 132652592 404088158 1166379692
## [565] 1112753628 1762627720 2094663322 1307027583 602362318 665566668
## [571] 2084155500 795722283 1323740512 176202264 51501835 155431104
## [577] 990450176 1350360135 895607449 761513520 1902678167 132965292
## [583] 1364669764 879373588 649434862 1539831580 623935063 313955540
## [589] 283440101 659048461 2054316448 1801948717 1537696625 1248968377
## [595] 1906346461 1656440434 1963858177 1888210096 1781231753 1240033491
## [601] 2061572749 1352031745 1073069308 508192050 641320231 448698124
## [607] 1454285451 1664188450 1188260622 1645840501 2051926947 296311056
## [613] 85340799 1951216244 2016123218 1985942560 1545764246 1550004763
## [619] 1953413631 292900881 752588043 68557871 1200903105 1527171229
## [625] 442296859 1242406946 1150041641 1397037287 1566969958 1472120945
## [631] 777625528 2114257101 2054673245 1356184955 9109427 630800652
## [637] 1887276572 1123879414 1922635733 552328122 1554424120 1067619085
## [643] 1248090910 43660474 1509662891 384919732 1125190960 343469238
## [649] 251439930 1850569861 521994326 687939087 140279761 1892382368
## [655] 1037646906 16851855 1908769228 1573696110 701924318 1114339655
## [661] 501696098 985520964 109472637 1660608227 1144994777 326256272
## [667] 863412713 830464612 1122512031 415866122 1550125116 1828702855
## [673] 222928121 1541449279 2042798392 1491509755 227840854 357890577
## [679] 2112716039 1923847975 1599126593 762806346 8884632 1147638381
## [685] 1807635760 483064211 1372008617 1816908080 1704123867 220432630
## [691] 401921335 1255807530 887873994 1781837802 688480799 654898757
## [697] 1029718024 2047601842 618715319 632547659 1184452163 2061579498
## [703] 1465462188 533046273 1754418674 1564180608 1836155729 929329913
## [709] 599283160 453765690 725521333 424896065 845038180 1247333649
## [715] 201276729 571240278 1583450256 1431098968 663508776 1856903008
## [721] 1736497252 1006551634 1384625219 1263256841 1534392445 1550189939
## [727] 770699369 1670419726 690617651 61748322 569446353 1497723839
## [733] 1588735586 67327104 1990238606 734965370 237036046 282659937
## [739] 431733995 1953494399 1650368657 847233547 1637644819 1746052981
## [745] 548415412 218016560 597222138 173907288 134545849 11803852
## [751] 818845040 1253377304 845254905 594863430 1333291225 1781245777
## [757] 1475734859 1387136010 512448238 1308111596 1641499633 2109402469
## [763] 2067251807 163195436 489075633 1474246762 2146493495 538384512
## [769] 1279888373 1887676659 1405690682 975691727 265727197 1458497866
## [775] 1595287004 655343433 2060936615 1397945842 1804668314 1323170
## [781] 763681720 1836393568 631722692 204133676 1343308273 486563400
## [787] 53336024 917874569 1342844782 1286604751 953208414 345807478
## [793] 895533964 1673934772 1785937304 869334209 1568800122 19432588
## [799] 185992172 1381728419 1968863122 106974831 482172078 1410314815
## [805] 1384083766 752990858 396218635 2047292745 1866172981 770627232
## [811] 458013167 1245906921 1992062997 1332733849 1003361933 1462411687
## [817] 802883494 1423129557 2013087860 362804535 949745912 133594833
## [823] 1207947116 1804263521 1787901807 1674481425 236116040 1999988271
## [829] 1388827853 1029966128 1922518476 729073370 2141923455 1039133524
## [835] 1380120464 713767201 441695065 1865473423 1898057808 1935486518
## [841] 1787106917 1199667077 80601456 1753973382 522608905 279750105
## [847] 918311452 95602775 478071469 1210856056 1302694220 785974375
## [853] 699407928 1771045865 1844505635 1679763000 956717538 1341596077
## [859] 1774456286 1181392913 36888629 1511897267 1430855165 860879049
## [865] 1196846704 2070716326 409307800 846073259 1464037226 206030056
## [871] 1003512228 1840936105 1816214406 782963184 1629928319 903856301
## [877] 1961015676 1358936023 1149152716 1489260341 1076645402 482061792
## [883] 1704221660 1864039581 1421795431 1065268648 399001897 1580936945
## [889] 2139553931 2016732949 1496273242 830871924 1525753874 243131491
## [895] 1797072643 1189899493 1273057987 906012448 1692156306 945097721
## [901] 1468343635 1716885768 2108821684 895932900 1936401183 2127496043
## [907] 1223272151 1674089126 85197688 1693433314 932934707 1055513802
## [913] 1805545994 1867589048 948145184 1147446748 734343576 523962523
## [919] 1555171361 741596690 20481642 637573574 1903143335 1508592927
## [925] 1729387607 1773832351 1432335603 2120280398 209010868 1709895631
## [931] 589706063 552769936 390057430 1575135366 1269179793 149715300
## [937] 1561696463 887320007 1060912881 206069926 1673607318 577385220
## [943] 1782275394 1600638602 405337845 695032631 1249873184 2081052181
## [949] 177847378 1931129069 1565905572 762854619 820208943 554174908
## [955] 381101717 1380322265 1957952961 1423492546 1671393042 2016754134
## [961] 1852329537 32097800 449329203 1323411969 1096831004 439058380
## [967] 500381568 367051724 1465291084 1952268639 376373160 1364359705
## [973] 2110662916 1776748066 1044633727 1480235464 1866876600 1858933530
## [979] 1503742154 1806824382 1878619694 1656618864 667763893 358210429
## [985] 1046017662 1117710892 1327501535 1110690062 1440012310 146192480
## [991] 335719192 992919275 2046317735 511565440 1503311139 1005206218
## [997] 247054977 1167108788 481768218 1065090736#A aprtir de la Asignacion de la mestr
#podemos calcular
#los siguientes
# 1 generar la media de la muestr a partir de la muestra generada
mean(muestr1)## [1] 1087077637# 1 Genrar la varianza de la muestr a partir de la muestra generada
var(muestr1)## [1] 3.92332e+17#las funciones de ggplot unicamente trabaja con data frame
## guardar en los resultados de muestr/m como dataframe
## en datos
v1 <- muestr1/m
v1## [1] 2.103997e-05 3.536188e-01 2.718817e-01 5.152727e-01 1.889107e-01
## [6] 2.208799e-02 2.329159e-01 6.168944e-01 1.445023e-01 6.495049e-01
## [11] 2.291173e-01 7.743672e-01 7.899391e-01 5.072334e-01 7.166996e-02
## [16] 5.570562e-01 4.438355e-01 5.426208e-01 8.271476e-01 8.693481e-01
## [21] 1.328178e-01 2.687839e-01 4.514626e-01 7.316542e-01 9.121413e-01
## [26] 3.586138e-01 2.229577e-01 2.496591e-01 2.047355e-02 9.894060e-02
## [31] 8.946288e-01 2.608401e-02 3.940271e-01 4.136127e-01 5.891229e-01
## [36] 3.877912e-01 6.070392e-01 5.084129e-01 8.949867e-01 4.219058e-02
## [41] 9.715940e-02 9.579681e-01 5.695820e-01 9.648882e-01 8.766921e-01
## [46] 5.637631e-01 1.662493e-01 1.514680e-01 7.221904e-01 8.544283e-01
## [51] 3.765415e-01 5.335488e-01 3.543382e-01 3.622369e-01 1.157654e-01
## [56] 6.695600e-01 2.948364e-01 3.149166e-01 8.039953e-01 7.496566e-01
## [61] 4.780116e-01 9.406710e-01 8.579532e-01 6.197933e-01 8.653805e-01
## [66] 4.505473e-01 3.485576e-01 2.072699e-01 5.843894e-01 8.321059e-01
## [71] 2.044653e-01 4.486639e-01 6.946741e-01 3.869824e-01 1.348108e-02
## [76] 5.764893e-01 5.570877e-02 2.972538e-01 9.446361e-01 4.989083e-01
## [81] 1.520360e-01 2.690774e-01 3.837657e-01 9.503466e-01 4.758738e-01
## [86] 1.015412e-02 6.602506e-01 8.322300e-01 2.903258e-01 5.053465e-01
## [91] 3.583295e-01 4.441923e-01 5.392945e-01 9.219519e-01 2.456884e-01
## [96] 2.849994e-01 9.848305e-01 4.545578e-02 9.752224e-01 5.623118e-01
## [101] 7.749155e-01 5.528081e-03 9.104609e-01 1.165812e-01 3.806467e-01
## [106] 5.297245e-01 7.931802e-02 9.796322e-02 4.677841e-01 4.717244e-02
## [111] 8.272187e-01 6.521728e-02 1.068461e-01 7.620153e-01 1.916205e-01
## [116] 5.655308e-01 8.758122e-01 7.759714e-01 7.516952e-01 7.404709e-01
## [121] 9.497331e-02 2.163810e-01 7.162808e-01 5.309700e-01 1.251570e-02
## [126] 3.514475e-01 7.786645e-01 1.367822e-02 8.898923e-01 4.198482e-01
## [131] 3.888796e-01 8.990877e-01 9.676081e-01 5.889966e-01 2.659764e-01
## [136] 2.657580e-01 5.939072e-01 7.990708e-01 9.836885e-01 8.531948e-01
## [141] 6.450216e-01 8.773271e-01 2.370055e-01 3.509807e-01 9.320327e-01
## [146] 6.742016e-01 3.055181e-01 8.427332e-01 8.170897e-01 8.274262e-01
## [151] 5.528822e-01 2.913763e-01 1.617451e-01 4.499095e-01 6.295388e-01
## [156] 6.580156e-01 2.682951e-01 2.354732e-01 5.978039e-01 2.901914e-01
## [161] 2.471729e-01 2.341654e-01 6.181580e-01 3.821301e-01 4.598724e-01
## [166] 7.582041e-02 3.137046e-01 4.326136e-01 9.362941e-01 2.951850e-01
## [171] 1.738854e-01 4.914173e-01 2.503529e-01 6.811220e-01 6.171753e-01
## [176] 8.650630e-01 1.133391e-01 8.908578e-01 6.465883e-01 2.096239e-01
## [181] 1.490182e-01 5.494305e-01 2.785472e-01 5.432763e-01 8.444293e-01
## [186] 3.237084e-01 5.677409e-01 2.194428e-02 8.175418e-01 4.247177e-01
## [191] 2.299664e-01 4.579070e-02 6.043072e-01 5.902826e-01 8.804830e-01
## [196] 2.783135e-01 6.149007e-01 6.355110e-01 3.268054e-02 2.618731e-01
## [201] 3.020304e-01 2.245971e-01 8.030104e-01 1.951168e-01 3.285487e-01
## [206] 9.174257e-01 1.740053e-01 5.072709e-01 7.015205e-01 4.551704e-01
## [211] 4.895507e-02 7.879377e-01 8.688800e-01 2.667454e-01 1.894415e-01
## [216] 9.434681e-01 8.676115e-01 9.465337e-01 3.923335e-01 9.494051e-01
## [221] 6.520821e-01 5.439701e-01 5.059387e-01 3.110998e-01 6.547606e-01
## [226] 5.607139e-01 9.187686e-01 7.432037e-01 2.537527e-02 4.821366e-01
## [231] 2.693031e-01 1.766356e-01 7.140011e-01 2.163532e-01 2.476378e-01
## [236] 4.821597e-02 3.658227e-01 3.815480e-01 6.764882e-01 7.376009e-01
## [241] 8.582734e-01 6.021359e-04 1.200981e-01 4.884788e-01 8.632080e-01
## [246] 9.366372e-01 6.105122e-02 8.777957e-02 3.112008e-01 3.514939e-01
## [251] 5.585700e-01 8.858045e-01 7.158544e-01 3.641445e-01 1.768549e-01
## [256] 4.009645e-01 1.065847e-02 1.368973e-01 8.321144e-01 3.475314e-01
## [261] 9.594312e-01 1.599638e-01 5.113940e-01 9.985810e-01 1.504154e-01
## [266] 3.129317e-02 9.442782e-01 4.829348e-01 6.850461e-01 5.700125e-01
## [271] 2.003588e-01 4.302926e-01 9.285271e-01 7.545624e-01 9.296883e-01
## [276] 2.709916e-01 5.550740e-01 1.284216e-01 3.814483e-01 1.942606e-03
## [281] 6.493742e-01 3.232588e-02 3.010755e-01 1.764469e-01 5.430537e-01
## [286] 1.030335e-01 6.840866e-01 4.434656e-01 3.263783e-01 4.396969e-01
## [291] 9.856935e-01 5.511851e-01 7.678918e-01 9.574970e-01 6.513781e-01
## [296] 7.123390e-01 2.816464e-01 6.311917e-01 4.380733e-01 6.980475e-01
## [301] 8.444928e-02 3.389723e-01 1.066788e-01 9.511670e-01 2.634711e-01
## [306] 1.584591e-01 2.222818e-01 8.898876e-01 3.409662e-01 6.195129e-01
## [311] 1.530453e-01 2.329284e-01 8.280107e-01 3.763374e-01 1.030711e-01
## [316] 3.164259e-01 1.705964e-01 2.139903e-01 5.357558e-01 4.474075e-01
## [321] 5.776037e-01 7.847035e-01 5.111611e-01 8.378411e-02 1.595594e-01
## [326] 7.154993e-01 3.963893e-01 1.141778e-01 9.862897e-01 5.707143e-01
## [331] 9.957930e-01 2.923147e-01 9.338201e-01 7.143895e-01 7.438817e-01
## [336] 4.190741e-01 3.779555e-01 2.978025e-01 1.665409e-01 5.313086e-02
## [341] 9.704423e-01 2.233244e-01 4.128153e-01 1.871073e-01 7.116947e-01
## [346] 4.524167e-01 7.668048e-01 6.878319e-01 3.902570e-01 4.955062e-02
## [351] 7.972379e-01 1.768921e-01 2.540704e-02 1.616105e-02 6.187392e-01
## [356] 1.501902e-01 2.471028e-01 5.603075e-02 7.087577e-01 9.055875e-02
## [361] 2.091346e-02 4.925038e-01 5.115499e-01 6.183563e-01 7.150051e-01
## [366] 9.002877e-02 1.134878e-01 3.896844e-01 4.262000e-01 1.437103e-01
## [371] 3.390891e-01 7.129318e-02 2.244356e-01 8.947509e-02 8.078252e-01
## [376] 1.180532e-01 1.196356e-01 7.157515e-01 6.350648e-01 5.333205e-01
## [381] 5.171320e-01 4.370126e-01 8.711358e-01 1.790790e-01 7.804711e-01
## [386] 3.775335e-01 2.050223e-01 8.098938e-01 8.846011e-01 4.913344e-01
## [391] 8.573766e-01 9.278993e-01 2.039044e-01 2.133258e-02 5.365883e-01
## [396] 4.400792e-01 4.105714e-01 4.729921e-01 5.782254e-01 2.343465e-01
## [401] 6.612852e-01 2.202938e-01 4.773015e-01 6.616209e-03 1.986275e-01
## [406] 3.330335e-01 2.944168e-01 2.630449e-01 9.953668e-01 1.301460e-01
## [411] 3.631433e-01 3.490732e-01 8.727042e-01 5.387994e-01 6.008935e-01
## [416] 2.170323e-01 6.615991e-01 4.953684e-01 6.565013e-01 8.166449e-01
## [421] 3.499957e-01 3.770234e-01 6.324713e-01 9.459535e-01 6.397774e-01
## [426] 7.385331e-01 5.260150e-01 7.348283e-01 2.598908e-01 9.846286e-01
## [431] 6.528264e-01 5.405355e-02 4.780095e-01 9.051784e-01 3.340840e-01
## [436] 9.496571e-01 8.870323e-01 3.511256e-01 3.686476e-01 8.599353e-01
## [441] 9.328984e-01 2.229055e-01 3.721822e-01 2.667425e-01 1.414267e-01
## [446] 9.591378e-01 2.289598e-01 1.279744e-01 8.653320e-01 6.347970e-01
## [451] 3.336163e-02 7.089321e-01 2.248885e-02 9.701832e-01 8.695152e-01
## [456] 9.412713e-01 9.463702e-01 6.433057e-01 3.824427e-02 7.714505e-01
## [461] 7.678318e-01 9.482632e-01 4.589837e-01 1.392260e-01 9.711845e-01
## [466] 6.976256e-01 9.941187e-01 1.536528e-01 4.426150e-01 2.955041e-02
## [471] 6.536686e-01 2.077684e-01 9.640438e-01 6.841819e-01 4.491293e-02
## [476] 8.516637e-01 9.119351e-01 8.929880e-01 4.488388e-01 6.345166e-01
## [481] 3.209560e-01 3.074732e-01 7.014941e-01 1.139961e-02 5.932918e-01
## [486] 4.549586e-01 4.890997e-01 2.988496e-01 7.656583e-01 4.196395e-01
## [491] 8.804356e-01 4.817300e-01 4.357479e-01 6.146073e-01 7.049531e-01
## [496] 1.469149e-01 1.981275e-01 9.294695e-01 5.943981e-01 4.833797e-02
## [501] 4.162140e-01 3.089746e-01 9.368235e-01 1.924129e-01 8.829668e-01
## [506] 2.303230e-02 1.038770e-01 8.613275e-01 3.320911e-01 4.549802e-01
## [511] 8.528224e-01 3.860158e-01 7.674020e-01 7.258705e-01 7.050271e-01
## [516] 3.909554e-01 7.872418e-01 1.734590e-01 3.261180e-01 6.456082e-02
## [521] 7.367680e-02 2.859450e-01 8.778933e-01 7.526026e-01 9.922411e-01
## [526] 5.957597e-01 9.332991e-01 9.579188e-01 7.419200e-01 4.491787e-01
## [531] 3.470540e-01 9.363618e-01 4.325912e-01 5.606362e-01 6.128919e-01
## [536] 8.740253e-01 7.437351e-01 9.557243e-01 8.591374e-01 5.226416e-01
## [541] 3.751801e-02 5.651554e-01 5.665455e-01 9.303709e-01 7.431810e-01
## [546] 6.433702e-01 1.226973e-01 1.735267e-01 4.636964e-01 3.451430e-01
## [551] 8.184685e-01 9.999204e-01 6.613856e-01 9.082538e-01 2.129708e-02
## [556] 9.400859e-01 2.448026e-02 4.397296e-01 5.358873e-01 6.576916e-01
## [561] 8.220421e-01 6.177118e-02 1.881682e-01 5.431379e-01 5.181663e-01
## [566] 8.207875e-01 9.754036e-01 6.086321e-01 2.804968e-01 3.099286e-01
## [571] 9.705105e-01 3.705371e-01 6.164147e-01 8.205057e-02 2.398241e-02
## [576] 7.237825e-02 4.612143e-01 6.288104e-01 4.170497e-01 3.546074e-01
## [581] 8.860036e-01 6.191679e-02 6.354739e-01 4.094902e-01 3.024167e-01
## [586] 7.170400e-01 2.905424e-01 1.461969e-01 1.319871e-01 3.068934e-01
## [591] 9.566156e-01 8.390978e-01 7.160458e-01 5.815962e-01 8.877117e-01
## [596] 7.713402e-01 9.144927e-01 8.792663e-01 8.294507e-01 5.774356e-01
## [601] 9.599946e-01 6.295888e-01 4.996868e-01 2.366454e-01 2.986380e-01
## [606] 2.089413e-01 6.772044e-01 7.749481e-01 5.533270e-01 7.664042e-01
## [611] 9.555029e-01 1.379806e-01 3.973991e-02 9.086059e-01 9.388305e-01
## [616] 9.247766e-01 7.198026e-01 7.217772e-01 9.096291e-01 1.363926e-01
## [621] 3.504511e-01 3.192475e-02 5.592141e-01 7.111445e-01 2.059605e-01
## [626] 5.785408e-01 5.355299e-01 6.505462e-01 7.296772e-01 6.855097e-01
## [631] 3.621101e-01 9.845277e-01 9.567818e-01 6.315228e-01 4.241908e-03
## [636] 2.937394e-01 8.788316e-01 5.233471e-01 8.952970e-01 2.571978e-01
## [641] 7.238351e-01 4.971489e-01 5.811876e-01 2.033099e-02 7.029916e-01
## [646] 1.792422e-01 5.239579e-01 1.599403e-01 1.170858e-01 8.617387e-01
## [651] 2.430725e-01 3.203466e-01 6.532285e-02 8.812092e-01 4.831920e-01
## [656] 7.847256e-03 8.888399e-01 7.328094e-01 3.268590e-01 5.189048e-01
## [661] 2.336205e-01 4.589190e-01 5.097717e-02 7.732810e-01 5.331797e-01
## [666] 1.519249e-01 4.020579e-01 3.867152e-01 5.227104e-01 1.936528e-01
## [671] 7.218333e-01 8.515561e-01 1.038090e-01 7.177933e-01 9.512521e-01
## [676] 6.945384e-01 1.060967e-01 1.666558e-01 9.838101e-01 8.958615e-01
## [681] 7.446513e-01 3.552094e-01 4.137229e-03 5.344108e-01 8.417460e-01
## [686] 2.249443e-01 6.388913e-01 8.460638e-01 7.935445e-01 1.026469e-01
## [691] 1.871592e-01 5.847810e-01 4.134485e-01 8.297329e-01 3.205989e-01
## [696] 3.049610e-01 4.794998e-01 9.534889e-01 2.881118e-01 2.945530e-01
## [701] 5.515535e-01 9.599978e-01 6.824090e-01 2.482190e-01 8.169649e-01
## [706] 7.283784e-01 8.550266e-01 4.327530e-01 2.790630e-01 2.113011e-01
## [711] 3.378472e-01 1.978576e-01 3.935016e-01 5.808350e-01 9.372678e-02
## [716] 2.660045e-01 7.373515e-01 6.664074e-01 3.089704e-01 8.646878e-01
## [721] 8.086195e-01 4.687121e-01 6.447664e-01 5.882498e-01 7.145072e-01
## [726] 7.218634e-01 3.588849e-01 7.778498e-01 3.215939e-01 2.875380e-02
## [731] 2.651691e-01 6.974320e-01 7.398127e-01 3.135163e-02 9.267771e-01
## [736] 3.422449e-01 1.103785e-01 1.316238e-01 2.010418e-01 9.096667e-01
## [741] 7.685128e-01 3.945239e-01 7.625878e-01 8.130693e-01 2.553758e-01
## [746] 1.015219e-01 2.781032e-01 8.098189e-02 6.265279e-02 5.496597e-03
## [751] 3.813044e-01 5.836493e-01 3.936025e-01 2.770049e-01 6.208621e-01
## [756] 8.294572e-01 6.871926e-01 6.459355e-01 2.386273e-01 6.091369e-01
## [761] 7.643828e-01 9.822671e-01 9.626391e-01 7.599380e-02 2.277436e-01
## [766] 6.864996e-01 9.995389e-01 2.507048e-01 5.959945e-01 8.790179e-01
## [771] 6.545757e-01 4.543419e-01 1.237389e-01 6.791660e-01 7.428634e-01
## [776] 3.051681e-01 9.596984e-01 6.509693e-01 8.403642e-01 6.161490e-04
## [781] 3.556170e-01 8.551374e-01 2.941688e-01 9.505715e-02 6.255267e-01
## [786] 2.265737e-01 2.483652e-02 4.274187e-01 6.253108e-01 5.991220e-01
## [791] 4.438723e-01 1.610292e-01 4.170155e-01 7.794866e-01 8.316419e-01
## [796] 4.048153e-01 7.305295e-01 9.049004e-03 8.660935e-02 6.434174e-01
## [801] 9.168233e-01 4.981404e-02 2.245289e-01 6.567290e-01 6.445142e-01
## [806] 3.506387e-01 1.845037e-01 9.533450e-01 8.690045e-01 3.588513e-01
## [811] 2.132790e-01 5.801706e-01 9.276266e-01 6.206026e-01 4.672268e-01
## [816] 6.809885e-01 3.738718e-01 6.626963e-01 9.374171e-01 1.689440e-01
## [821] 4.422599e-01 6.220994e-02 5.624942e-01 8.401757e-01 8.325567e-01
## [826] 7.797412e-01 1.099501e-01 9.313171e-01 6.467234e-01 4.796154e-01
## [831] 8.952424e-01 3.395012e-01 9.974108e-01 4.838843e-01 6.426687e-01
## [836] 3.323738e-01 2.056803e-01 8.686788e-01 8.838520e-01 9.012811e-01
## [841] 8.321865e-01 5.586385e-01 3.753298e-02 8.167575e-01 2.433587e-01
## [846] 1.302688e-01 4.276221e-01 4.451851e-02 2.226194e-01 5.638488e-01
## [851] 6.066143e-01 3.659978e-01 3.256872e-01 8.247075e-01 8.589149e-01
## [856] 7.822006e-01 4.455063e-01 6.247294e-01 8.262956e-01 5.501289e-01
## [861] 1.717761e-02 7.040320e-01 6.662939e-01 4.008780e-01 5.573252e-01
## [866] 9.642524e-01 1.905988e-01 3.939836e-01 6.817455e-01 9.594022e-02
## [871] 4.672968e-01 8.572527e-01 8.457407e-01 3.645956e-01 7.589945e-01
## [876] 4.208909e-01 9.131691e-01 6.328039e-01 5.351159e-01 6.934909e-01
## [881] 5.013521e-01 2.244775e-01 7.935901e-01 8.680111e-01 6.620751e-01
## [886] 4.960544e-01 1.857997e-01 7.361811e-01 9.963074e-01 9.391145e-01
## [891] 6.967565e-01 3.869049e-01 7.104845e-01 1.132169e-01 8.368272e-01
## [896] 5.540901e-01 5.928138e-01 4.218949e-01 7.879717e-01 4.400954e-01
## [901] 6.837508e-01 7.994872e-01 9.819966e-01 4.172013e-01 9.017071e-01
## [906] 9.906925e-01 5.696305e-01 7.795585e-01 3.967327e-02 7.885663e-01
## [911] 4.344316e-01 4.915119e-01 8.407729e-01 8.696639e-01 4.415145e-01
## [916] 5.343215e-01 3.419554e-01 2.439891e-01 7.241831e-01 3.453329e-01
## [921] 9.537508e-03 2.968933e-01 8.862202e-01 7.024933e-01 8.053089e-01
## [926] 8.260051e-01 6.669832e-01 9.873325e-01 9.732827e-02 7.962322e-01
## [931] 2.746033e-01 2.574036e-01 1.816346e-01 7.334796e-01 5.910079e-01
## [936] 6.971662e-02 7.272216e-01 4.131906e-01 4.940261e-01 9.595879e-02
## [941] 7.793341e-01 2.688659e-01 8.299367e-01 7.453554e-01 1.887501e-01
## [946] 3.236498e-01 5.820176e-01 9.690654e-01 8.281664e-02 8.992520e-01
## [951] 7.291816e-01 3.552319e-01 3.819396e-01 2.580578e-01 1.774643e-01
## [956] 6.427626e-01 9.117429e-01 6.628654e-01 7.783030e-01 9.391243e-01
## [961] 8.625582e-01 1.494670e-02 2.092352e-01 6.162617e-01 5.107517e-01
## [966] 2.044525e-01 2.330083e-01 1.709218e-01 6.823293e-01 9.090959e-01
## [971] 1.752624e-01 6.353295e-01 9.828540e-01 8.273628e-01 4.864455e-01
## [976] 6.892884e-01 8.693322e-01 8.656334e-01 7.002345e-01 8.413682e-01
## [981] 8.748005e-01 7.714233e-01 3.109518e-01 1.668047e-01 4.870899e-01
## [986] 5.204747e-01 6.181661e-01 5.172054e-01 6.705580e-01 6.807618e-02
## [991] 1.563314e-01 4.623641e-01 9.528910e-01 2.382162e-01 7.000338e-01
## [996] 4.680856e-01 1.150439e-01 5.434774e-01 2.243408e-01 4.959715e-01dat1<- data.frame(v1)
## generando graficos ...
ggplot(dat1, aes(v1))+geom_histogram(binwidth = 0.1,col="black",fill="pink",alpha=0.4,) + labs(y="Conteo",x="Valor de datos muestr/m",title = "Valores generados con operador congrencial multiplicativo")+ theme_bw()
Probar que provenga de una distribucion uniforme [0,1] DECISION DE HIPOTESIS A PROVAR \[H_0: U\sim Uniforme(0,1)\] \[H_1: U\nsim Uniforme(0,1)\]
ks.test(v1,punif,0,1)##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: v1
## D = 0.022005, p-value = 0.7181
## alternative hypothesis: two-sidedDe acuerdo a los resultados, p-valor = 0.71, si alpha es mayor que p-valor se rechaza Ho. Note que p-valor es mayor que alpha Por lo tanto NO RECHAZA. es decir, la muestra simulada proviene de una distribución uniforme ########################################################################################### ##########################################################################################
Prueba de independencia de la muestra generada (autocorrelacion) autocorrelacion (ACF) mide la autocorrelacion de una seriel temporal en diferentes intervalos de tiempo.
prueIND1<- acf(v1, type= "correlation");prueIND1 # Ver si hay independencia en la muestra generada
##
## Autocorrelations of series 'v1', by lag
##
## 0 1 2 3 4 5 6 7 8 9 10
## 1.000 0.053 -0.032 0.013 0.077 -0.007 0.047 0.002 -0.006 -0.026 -0.003
## 11 12 13 14 15 16 17 18 19 20 21
## -0.028 -0.006 0.030 0.008 0.042 -0.009 -0.006 0.036 -0.013 0.014 0.005
## 22 23 24 25 26 27 28 29 30
## 0.035 0.003 -0.001 -0.029 0.000 0.032 -0.026 -0.043 0.002No hay correlación en los datos de la muestra generada de una uniforme Como en el gráfico se ve que las barras salen del rango, Por lo tanto se concluye , que la muesta es independiente. ################################################ Con el estadístico Ljung-Box, se puede probar \(H_{0}\): Muestra aleatoria \(H_{1}\): Muestra no aleatoria
Se rechaza \(H_{0}\) si \(p-valor <\alpha\)
Box.test(v1, lag = 10, type = "Ljung")##
## Box-Ljung test
##
## data: v1
## X-squared = 12.948, df = 10, p-value = 0.2266De acuerdo a los resultados, p-valor = 0.2266, Note que \(p-valor > \alpha\), llegamos a conclusion ,que No se rechaza \(H0\) Por lo tanto La muestra generada es aleatoria
#######################################################################################3
- \(c=0\), \(a=48271\) y \(m=2^{31}-1\)
rm(list=ls())
n <- 1000 # numero de numeros aleatorios a generar (1000)
a <- 48271 #valor de operacion
m <- 2^{31}-1 #valor del modulo
c <- 0
muestr2 <-45183 # Fijar un valor a la semilla asignamos el valor de muestr
# Enseguida se utiliza el ciclo for para generar los valores aleatorios en n muestra
#iniciando en la posicion 2,tomara el valor de 2-1, pues en este caso la semilla inicial 45183, sera el primer posicion.
for(i in 2:n)
{
muestr2[i]<-(a*muestr2[i-1]+c)%%m
}
muestr2## [1] 45183 33544946 45418528 1964445148 1443822176 305977958
## [7] 1616970199 327842067 457421414 1909700387 264349755 79193131
## [13] 210734841 1898957719 1396065301 1431301711 1521000397 2039239951
## [19] 1943747182 912201245 861599307 2091840395 546625105 8872766
## [25] 948041833 50803173 2041122656 482003416 949062138 2057305594
## [31] 2112039753 632259385 1902665818 1085782 872175394 1509027986
## [37] 1792089613 1021440669 1885481826 1588779339 1031471205 738180860
## [43] 1679622036 937690918 765474959 638115607 1120516576 1932506754
## [49] 1638863948 599045722 668739807 1912525640 1350667557 470121027
## [55] 752396468 686468764 861033834 565696976 1504156891 735180391
## [61] 725387286 448818171 1086901405 644740898 954875034 1331250653
## [67] 1647101782 963056041 1099648502 1779537143 691549753 1312318095
## [73] 434144539 1445614643 930806635 1314215551 1831929941 8565845
## [79] 1165043771 1673605952 445592499 2146794524 1095082019 394168244
## [85] 190193704 347694859 993837484 891999831 676719851 570173104
## [91] 675483232 1006879471 1229045737 883538705 271599635 2145799797
## [97] 323255236 237317854 892357336 753974530 1699171921 1884868720
## [103] 2058310671 1235987739 973468315 1199353358 2121788192 900239661
## [109] 1137079086 410026633 1186310791 1756745106 8758990 1898411478
## [115] 798269754 980217213 557894372 674297432 1749186140 202131194
## [121] 1056657253 1018159666 274492244 41008134 1671197427 147799162
## [127] 472673568 1559535200 284393615 1248718041 1297553115 678365763
## [133] 563096317 521797828 2014743372 585388123 680258107 1714120367
## [139] 1906800194 2003054154 1123345206 1034352076 214267846 641950314
## [145] 1542064531 918803587 1735670233 610813085 1755436372 1259369486
## [151] 57379430 1656044547 995052309 1550758937 1847164448 954045968
## [157] 2113595060 546555937 965031532 1969294095 1431625290 2108096777
## [163] 1426909472 2104112681 236656039 1158140176 1290136992 1324461479
## [169] 344397972 763594985 84203827 1563872993 1368085759 1598043792
## [175] 1559283392 1014271529 1568792053 445346202 995210272 585856322
## [181] 1805855566 1945311009 1237766717 947169473 890786553 92635982
## [187] 570534068 919707300 261643869 459872492 2114085940 619504300
## [193] 382280825 1898208551 1740198772 164587160 1244790107 670811937
## [199] 1004581461 1970954671 2132394447 1773666780 791098784 575191510
## [205] 253307147 1764890466 203924149 1705042178 1780202963 619092268
## [211] 1967920623 1704751435 630649492 1500932107 1837938158 120916307
## [217] 2037986298 1558205335 514989610 1940250285 1764694271 1470813539
## [223] 1830971249 976184547 1318085763 1819856104 1307932002 1313930389
## [229] 951776921 2106093320 1354800740 267018449 50702385 1470952402
## [235] 2091576181 677652993 516713999 1426369471 1807528174 1079393191
## [241] 1140479247 1330441092 1223488397 1060635440 1923179760 239618797
## [247] 292027245 364484487 1844635753 1297977502 1836597817 1993308953
## [253] 1011666428 372013208 191307154 407948634 1810952471 1017392859
## [259] 1914657193 1163647364 839636712 644855121 26082526 604195404
## [265] 140936577 2068798318 679055384 1639536903 871001822 694108796
## [271] 285831222 1923968834 1821787852 66059242 1879938434 291676335
## [277] 605577053 262522399 2065204829 1163923272 1273089898 930423806
## [283] 14546068 2073579506 1691031103 1908950443 571024930 991786785
## [289] 686956164 765999117 169942661 2062141238 1457693754 2033505379
## [295] 8128986 1552259452 1264080015 1953541854 1264411017 751470220
## [301] 1072708143 569074289 1321675542 1155902806 664232072 1215497802
## [307] 1893680655 69979303 2126642029 1124087965 380849766 1539036266
## [313] 770311768 40005323 509147880 1274459212 456586843 278829292
## [319] 1088738383 1270676409 393013225 270846377 145021231 1670636028
## [325] 965795444 189384601 2093673239 973008302 468902305 2053008922
## [331] 865815753 1612958796 2114419731 1699544132 524513078 2086073655
## [337] 1353192675 2101007773 683497261 1305016870 184030672 1352204120
## [343] 1627109602 140692764 1037119230 643572466 388068784 2115903330
## [349] 299907463 645882046 204655320 492175520 192939159 1877050697
## [355] 484160663 2002317019 2048323620 187385846 101051102 902382305
## [361] 1485432554 983324451 223524580 797158652 1033303746 1149937944
## [367] 497187168 1592031303 1240719218 1733424542 1730728821 454599250
## [373] 972491704 1302004011 779201879 1825307651 319068658 10474034
## [379] 933438169 1639458092 1361683335 1784280056 2003436594 256753623
## [385] 626008996 837848979 248541358 1496239876 825038492 348813717
## [391] 1315140827 1398771150 1048836323 1451169508 634239175 832344793
## [397] 843951180 602626190 1702818875 1833326200 835390977 1857411048
## [403] 1646435758 1025666242 1847169644 1204862084 1745528710 1895470365
## [409] 561724833 890886721 632878216 1709485961 1537687456 86413668
## [415] 860925554 1781364037 830720500 1894598716 1436028894 2073584408
## [421] 1927655545 1541871832 206964746 301328322 512690131 463765473
## [427] 1053610855 2141853451 955232053 1385045626 2076514242 1619751857
## [433] 1457269271 870639309 375112949 1642533322 1629739022 363890411
## [439] 1085280568 1862213010 1513709584 144240089 471352545 69459730
## [445] 668653863 2058890110 1288800297 1225366544 1526356103 719002990
## [451] 1510111123 389104565 574480453 289613052 1940574769 247992259
## [457] 760485811 325120963 103512697 1614433965 307858532 52360932
## [463] 2073779700 617177442 1879151598 965021425 1481419098 523318105
## [469] 238106794 320574430 1828633895 1966402904 1457381584 1997132838
## [475] 910825621 1030846260 636231823 382692286 285006012 744962570
## [481] 474547455 1819621403 716098266 882615974 827608121 1980807297
## [487] 987134459 1600310753 1466091826 1542429608 1361566278 428788903
## [493] 621746927 1261946392 2040641077 858023624 1288738062 368704506
## [499] 1538226437 333761755 591355811 983716857 1985485430 1319509567
## [505] 1828822284 322710088 1839766157 313426509 388722824 1474813465
## [511] 1637870965 2058887210 1148814397 2097024753 1692667071 1421866832
## [517] 1356489352 173629715 1798782171 1955360837 1021709883 1995808938
## [523] 1429358131 44247038 1250026180 18221374 1243132731 124509980
## [529] 1562000274 1164380084 1849025480 593608466 199960365 1495269297
## [535] 1218859817 972749548 863489853 1008589540 23924203 1646484574
## [541] 1234579731 1726990851 407675728 1522408827 1306087777 338174941
## [547] 1019376164 1014008733 1768268219 42682040 867935367 849631134
## [553] 2049262555 413560644 2125347659 920579458 1559393394 2029210777
## [559] 1009309603 422346924 1046107433 721422785 204434983 593706428
## [565] 633716773 1385281615 583037379 1024127774 598224814 1844879032
## [571] 156396229 997350854 834674988 1655644381 1005992146 1346653602
## [577] 2133511099 1988484297 48930528 1840989035 1360911978 1057328308
## [583] 1198400866 1241203447 1485322484 2112586422 1250714920 1052135209
## [589] 1777905736 1398797395 168225071 756732934 1706105291 1558123058
## [595] 838363837 1478931759 716061468 1253823363 775931972 749933085
## [601] 2035592203 1956962528 1027524852 1369819780 1549109250 1672018210
## [607] 1113109709 877915199 1549764678 1097928493 357361290 1598176886
## [613] 1541412925 1677385066 331094398 684384884 1201793763 1810977362
## [619] 71422673 932594948 1738526494 1046434408 1472447481 1246090592
## [625] 1169497609 1916455350 2063138031 181764776 1496804301 153110256
## [631] 1293938049 121690284 743924419 1901568062 698397081 1127206345
## [637] 584315456 441156878 635814286 1702600229 2016483369 824921077
## [643] 1123525193 1132569965 1793578836 2040763751 337169337 1869989361
## [649] 1076310480 511308209 329001668 597946463 1293499793 441471378
## [655] 784658257 1069641508 715907847 280835013 1270132659 2062944386
## [661] 1571745216 1263556673 313620289 1152742616 590039519 1869495135
## [667] 841847351 2127911587 129896420 1725324227 1562447210 1263591270
## [673] 1983652076 868508160 581634626 2031314415 1622288092 1477301077
## [679] 1458305585 1502428522 1056942625 1908449596 16959510 461237703
## [685] 1442193064 1124007545 793863240 874260972 1250232215 1373802271
## [691] 514404081 1593467337 1840039728 634070368 1273796684 687952460
## [697] 1613563099 1219958786 333990972 918471383 732236478 353683565
## [703] 164372465 1618665997 581328739 150744920 933437284 1596738257
## [709] 816829170 1361106150 1840270332 1028137817 893482237 1366979526
## [715] 1886161824 53224445 806742783 1959907142 1433066544 811908260
## [721] 47060710 1777317531 922841251 1216737300 1595946497 1252487856
## [727] 734182985 1971726141 717317171 1738320760 1852866729 1330945303
## [733] 1939937461 1696752496 1060921483 698375884 104005958 1802315579
## [739] 717806645 1743400097 76923651 182331758 948305012 2017298447
## [745] 1514845569 1292280849 1731367670 1227708271 747226829 250927647
## [751] 720679257 820816894 579003124 1707616546 1493469165 224033925
## [757] 1761431030 717213459 1027006102 2099042294 297140920 246071007
## [763] 361527340 834113618 327556875 1723303911 676537689 366965790
## [769] 1360528634 1880282907 1887346989 1427749338 1843095074 2089789138
## [775] 314646220 1283334036 1503970394 322718292 88297794 1615258526
## [781] 1455536917 1000041608 1871042502 372872163 851734666 509640671
## [787] 1439653456 941157656 604660491 1116314684 966440840 1278523859
## [793] 1240150303 41132341 1224342583 1490858553 908717246 189208044
## [799] 13541233 813829455 443267734 1597212853 103732569 1490457042
## [805] 854732588 1340929184 688036637 1381903772 739935098 459098654
## [811] 1267373841 2036026822 1461619807 421965159 1945281941 1982108936
## [817] 1541524865 638389865 1474322612 1566225919 1129543414 1727823511
## [823] 1946300942 1778182326 1865171403 436893738 1008213458 1197422804
## [829] 1273812879 1469701305 1829415010 1016899423 1718328154 1009940006
## [835] 787759079 425564980 1766066025 1114757816 976793257 636355115
## [841] 2039153124 2047488359 670691408 1628977043 89624101 1212914313
## [847] 1740134662 1364900644 320696564 1281713268 577289558 596450746
## [853] 2108188484 1558730775 108700086 759301685 1148233286 1963503083
## [859] 1066559148 103679930 1097003520 805146194 52887168 1705913892
## [865] 909036517 568352956 861948651 1775155443 1783390106 1994333084
## [871] 1055370048 1160512874 2006008859 2015989559 610538684 1394727583
## [877] 1282825543 580824908 1600122483 968045244 1415298051 2102441457
## [883] 1169380921 578776196 1490993293 970300845 773747925 550499051
## [889] 177042843 1197643040 1167406600 1913091320 739319426 804766600
## [895] 1056858017 2119304122 1250780923 2090682375 482416507 1562024976
## [901] 209286679 714206521 1907989900 1449294011 296436662 610571441
## [907] 828457083 11379059 1670227004 549150763 1665825852 702023624
## [913] 90404444 226145620 615845319 2000751675 1649531041 114216645
## [919] 761148946 123055843 88829851 1528378209 1691317601 706109872
## [925] 1916669775 1676228971 359807475 1566372436 1759614580 1082185036
## [931] 614159481 80560516 1791266766 2103982425 391519604 1186711084
## [937] 1751935686 1928963693 262974530 267700213 747877724 1605509134
## [943] 1141554378 1688482065 1270905024 691069655 1759827654 630061855
## [949] 1052393891 1379842676 33017844 371481650 302274700 1098145982
## [955] 118354574 787140534 632550343 915113907 1872269654 1626667886
## [961] 293456198 621998046 498809759 459226525 997383941 284333918
## [967] 514567801 906460869 793299874 1597308197 411115499 59870302
## [973] 1633842627 880511842 190783758 912904082 428505782 1987598665
## [979] 248261196 857441856 1123502345 29674157 29639998 528234556
## [985] 1336911845 40593998 1007791394 151324283 982581246 855498024
## [991] 1782068341 468440532 1237600909 1533386093 761234054 2083820464
## [997] 2111075911 1351282437 86222449 220527793#A aprtir de la Asignacion de la mestr
#podemos calcular
#los siguientes
# 1 generar la media de la muestr a partir de la muestra generada
mean(muestr2)## [1] 1081210502# 1 Genrar la varianza de la muestr a partir de la muestra generada
var(muestr2)## [1] 3.790225e+17#las funciones de ggplot unicamente trabaja con data frame
## guardar en los resultados de muestr/m como dataframe
## en datos
v2 <- muestr2/m
v2## [1] 2.103997e-05 1.562058e-02 2.114965e-02 9.147661e-01 6.723321e-01
## [6] 1.424821e-01 7.529604e-01 1.526634e-01 2.130034e-01 8.892735e-01
## [11] 1.230974e-01 3.687718e-02 9.813106e-02 8.842711e-01 6.500936e-01
## [16] 6.665018e-01 7.082710e-01 9.495951e-01 9.051278e-01 4.247768e-01
## [21] 4.012134e-01 9.740891e-01 2.545422e-01 4.131704e-03 4.414664e-01
## [26] 2.365707e-02 9.504718e-01 2.244503e-01 4.419415e-01 9.580076e-01
## [31] 9.834952e-01 2.944187e-01 8.859978e-01 5.056066e-04 4.061383e-01
## [36] 7.026959e-01 8.345068e-01 4.756454e-01 8.779959e-01 7.398330e-01
## [41] 4.803162e-01 3.437422e-01 7.821350e-01 4.366464e-01 3.564521e-01
## [46] 2.971457e-01 5.217812e-01 8.998936e-01 7.631555e-01 2.789524e-01
## [51] 3.114062e-01 8.905892e-01 6.289536e-01 2.189172e-01 3.503619e-01
## [56] 3.196619e-01 4.009501e-01 2.634232e-01 7.004276e-01 3.423450e-01
## [61] 3.377848e-01 2.089972e-01 5.061279e-01 3.002309e-01 4.446483e-01
## [66] 6.199119e-01 7.669915e-01 4.484579e-01 5.120637e-01 8.286616e-01
## [71] 3.220279e-01 6.110957e-01 2.021643e-01 6.731668e-01 4.334406e-01
## [76] 6.119793e-01 8.530589e-01 3.988782e-03 5.425158e-01 7.793335e-01
## [81] 2.074952e-01 9.996791e-01 5.099373e-01 1.835489e-01 8.856585e-02
## [86] 1.619080e-01 4.627916e-01 4.153698e-01 3.151222e-01 2.655075e-01
## [91] 3.145464e-01 4.688648e-01 5.723190e-01 4.114298e-01 1.264734e-01
## [96] 9.992159e-01 1.505274e-01 1.105097e-01 4.155363e-01 3.510968e-01
## [101] 7.912386e-01 8.777104e-01 9.584756e-01 5.755516e-01 4.533065e-01
## [106] 5.584924e-01 9.880346e-01 4.192068e-01 5.294937e-01 1.909335e-01
## [111] 5.524190e-01 8.180482e-01 4.078723e-03 8.840167e-01 3.717233e-01
## [116] 4.564492e-01 2.597898e-01 3.139942e-01 8.145283e-01 9.412467e-02
## [121] 4.920444e-01 4.741175e-01 1.278204e-01 1.909590e-02 7.782119e-01
## [126] 6.882435e-02 2.201058e-01 7.262152e-01 1.324311e-01 5.814797e-01
## [131] 6.042203e-01 3.158887e-01 2.622122e-01 2.429810e-01 9.381880e-01
## [136] 2.725926e-01 3.167699e-01 7.981995e-01 8.879230e-01 9.327448e-01
## [141] 5.230984e-01 4.816577e-01 9.977624e-02 2.989314e-01 7.180798e-01
## [146] 4.278513e-01 8.082344e-01 2.844320e-01 8.174388e-01 5.864396e-01
## [151] 2.671938e-02 7.711558e-01 4.633573e-01 7.221284e-01 8.601530e-01
## [156] 4.442623e-01 9.842194e-01 2.545099e-01 4.493778e-01 9.170240e-01
## [161] 6.666525e-01 9.816591e-01 6.644565e-01 9.798038e-01 1.102016e-01
## [166] 5.393010e-01 6.007669e-01 6.167504e-01 1.603728e-01 3.555766e-01
## [171] 3.921046e-02 7.282351e-01 6.370646e-01 7.441471e-01 7.260979e-01
## [176] 4.723070e-01 7.305257e-01 2.073805e-01 4.634309e-01 2.728106e-01
## [181] 8.409170e-01 9.058560e-01 5.763800e-01 4.410602e-01 4.148048e-01
## [186] 4.313699e-02 2.656756e-01 4.282721e-01 1.218374e-01 2.141448e-01
## [191] 9.844480e-01 2.884792e-01 1.780134e-01 8.839222e-01 8.103432e-01
## [196] 7.664187e-02 5.796506e-01 3.123712e-01 4.677947e-01 9.177973e-01
## [201] 9.929735e-01 8.259280e-01 3.683841e-01 2.678444e-01 1.179553e-01
## [206] 8.218412e-01 9.495958e-02 7.939721e-01 8.289716e-01 2.882873e-01
## [211] 9.163845e-01 7.938367e-01 2.936691e-01 6.989260e-01 8.558566e-01
## [216] 5.630604e-02 9.490113e-01 7.255959e-01 2.398107e-01 9.034994e-01
## [221] 8.217498e-01 6.849009e-01 8.526124e-01 4.545714e-01 6.137815e-01
## [226] 8.474365e-01 6.090533e-01 6.118465e-01 4.432057e-01 9.807261e-01
## [231] 6.308783e-01 1.243402e-01 2.361014e-02 6.849656e-01 9.739661e-01
## [236] 3.155568e-01 2.406137e-01 6.642050e-01 8.416959e-01 5.026316e-01
## [241] 5.310770e-01 6.195349e-01 5.697312e-01 4.938969e-01 8.955504e-01
## [246] 1.115812e-01 1.359858e-01 1.697263e-01 8.589755e-01 6.044179e-01
## [251] 8.552325e-01 9.282068e-01 4.710939e-01 1.732321e-01 8.908434e-02
## [256] 1.899659e-01 8.432905e-01 4.737605e-01 8.915817e-01 5.418655e-01
## [261] 3.909863e-01 3.002841e-01 1.214562e-02 2.813504e-01 6.562871e-02
## [266] 9.633593e-01 3.162098e-01 7.634689e-01 4.055918e-01 3.232196e-01
## [271] 1.331005e-01 8.959178e-01 8.483361e-01 3.076123e-02 8.754146e-01
## [276] 1.358224e-01 2.819938e-01 1.222465e-01 9.616859e-01 5.419940e-01
## [281] 5.928287e-01 4.332623e-01 6.773541e-03 9.655857e-01 7.874477e-01
## [286] 8.889243e-01 2.659042e-01 4.618367e-01 3.198889e-01 3.566961e-01
## [291] 7.913572e-02 9.602593e-01 6.787916e-01 9.469247e-01 3.785354e-03
## [296] 7.228271e-01 5.886331e-01 9.096888e-01 5.887873e-01 3.499306e-01
## [301] 4.995187e-01 2.649959e-01 6.154531e-01 5.382592e-01 3.093072e-01
## [306] 5.660103e-01 8.818138e-01 3.258665e-02 9.902949e-01 5.234442e-01
## [311] 1.773470e-01 7.166696e-01 3.587044e-01 1.862893e-02 2.370905e-01
## [316] 5.934663e-01 2.126148e-01 1.298400e-01 5.069833e-01 5.917048e-01
## [321] 1.830110e-01 1.261227e-01 6.753077e-02 7.779505e-01 4.497335e-01
## [326] 8.818908e-02 9.749426e-01 4.530923e-01 2.183497e-01 9.560068e-01
## [331] 4.031769e-01 7.510925e-01 9.846034e-01 7.914119e-01 2.442454e-01
## [336] 9.714037e-01 6.301294e-01 9.783580e-01 3.182782e-01 6.076958e-01
## [341] 8.569596e-02 6.296691e-01 7.576820e-01 6.551517e-02 4.829463e-01
## [346] 2.996868e-01 1.807086e-01 9.852943e-01 1.396553e-01 3.007623e-01
## [351] 9.530006e-02 2.291871e-01 8.984430e-02 8.740698e-01 2.254549e-01
## [356] 9.324015e-01 9.538250e-01 8.725833e-02 4.705559e-02 4.202045e-01
## [361] 6.917084e-01 4.578961e-01 1.040867e-01 3.712059e-01 4.811696e-01
## [366] 5.354816e-01 2.315208e-01 7.413473e-01 5.777549e-01 8.071887e-01
## [371] 8.059334e-01 2.116893e-01 4.528517e-01 6.062929e-01 3.628442e-01
## [376] 8.499751e-01 1.485779e-01 4.877352e-03 4.346660e-01 7.634322e-01
## [381] 6.340832e-01 8.308701e-01 9.329229e-01 1.195602e-01 2.915082e-01
## [386] 3.901538e-01 1.157361e-01 6.967410e-01 3.841885e-01 1.624290e-01
## [391] 6.124102e-01 6.513536e-01 4.884025e-01 6.757535e-01 2.953406e-01
## [396] 3.875907e-01 3.929954e-01 2.806197e-01 7.929368e-01 8.537090e-01
## [401] 3.890092e-01 8.649244e-01 7.666814e-01 4.776131e-01 8.601554e-01
## [406] 5.610576e-01 8.128251e-01 8.826472e-01 2.615735e-01 4.148515e-01
## [411] 2.947069e-01 7.960414e-01 7.160415e-01 4.023950e-02 4.008997e-01
## [416] 8.295123e-01 3.868344e-01 8.822413e-01 6.687031e-01 9.655880e-01
## [421] 8.976346e-01 7.179900e-01 9.637547e-02 1.403169e-01 2.387399e-01
## [426] 2.159576e-01 4.906258e-01 9.973782e-01 4.448146e-01 6.449621e-01
## [431] 9.669523e-01 7.542557e-01 6.785939e-01 4.054230e-01 1.746756e-01
## [436] 7.648642e-01 7.589064e-01 1.694497e-01 5.053731e-01 8.671605e-01
## [441] 7.048760e-01 6.716703e-02 2.194906e-01 3.234471e-02 3.113662e-01
## [446] 9.587454e-01 6.001444e-01 5.706058e-01 7.107649e-01 3.348119e-01
## [451] 7.032003e-01 1.811909e-01 2.675133e-01 1.348616e-01 9.036505e-01
## [456] 1.154804e-01 3.541288e-01 1.513962e-01 4.820186e-02 7.517794e-01
## [461] 1.433578e-01 2.438246e-02 9.656789e-01 2.873956e-01 8.750482e-01
## [466] 4.493731e-01 6.898395e-01 2.436890e-01 1.108771e-01 1.492791e-01
## [471] 8.515240e-01 9.156777e-01 6.786462e-01 9.299874e-01 4.241362e-01
## [476] 4.800252e-01 2.962685e-01 1.782050e-01 1.327163e-01 3.469002e-01
## [481] 2.209784e-01 8.473272e-01 3.334592e-01 4.110001e-01 3.853851e-01
## [486] 9.223853e-01 4.596703e-01 7.452028e-01 6.827022e-01 7.182498e-01
## [491] 6.340287e-01 1.996704e-01 2.895235e-01 5.876396e-01 9.502476e-01
## [496] 3.995484e-01 6.001154e-01 1.716914e-01 7.162925e-01 1.554199e-01
## [501] 2.753715e-01 4.580789e-01 9.245637e-01 6.144445e-01 8.516117e-01
## [506] 1.502736e-01 8.567079e-01 1.459506e-01 1.810132e-01 6.867635e-01
## [511] 7.626931e-01 9.587441e-01 5.349584e-01 9.765032e-01 7.882095e-01
## [516] 6.621083e-01 6.316646e-01 8.085264e-02 8.376232e-01 9.105358e-01
## [521] 4.757707e-01 9.293710e-01 6.655967e-01 2.060413e-02 5.820888e-01
## [526] 8.484988e-03 5.788788e-01 5.797948e-02 7.273631e-01 5.422067e-01
## [531] 8.610196e-01 2.764205e-01 9.311380e-02 6.962890e-01 5.675758e-01
## [536] 4.529718e-01 4.020938e-01 4.696611e-01 1.114058e-02 7.667041e-01
## [541] 5.748960e-01 8.041928e-01 1.898388e-01 7.089269e-01 6.081945e-01
## [546] 1.574750e-01 4.746840e-01 4.721846e-01 8.234141e-01 1.987537e-02
## [551] 4.041639e-01 3.956403e-01 9.542622e-01 1.925792e-01 9.896921e-01
## [556] 4.286782e-01 7.261491e-01 9.449249e-01 4.699964e-01 1.966706e-01
## [561] 4.871317e-01 3.359387e-01 9.519746e-02 2.764661e-01 2.950974e-01
## [566] 6.450720e-01 2.714979e-01 4.768967e-01 2.785701e-01 8.590887e-01
## [571] 7.282767e-02 4.644277e-01 3.886758e-01 7.709695e-01 4.684516e-01
## [576] 6.270845e-01 9.934935e-01 9.259602e-01 2.278505e-02 8.572773e-01
## [581] 6.337240e-01 4.923569e-01 5.580489e-01 5.779804e-01 6.916572e-01
## [586] 9.837497e-01 5.824095e-01 4.899386e-01 8.279019e-01 6.513658e-01
## [591] 7.833590e-02 3.523812e-01 7.944672e-01 7.255576e-01 3.903936e-01
## [596] 6.886813e-01 3.334421e-01 5.838570e-01 3.613215e-01 3.492148e-01
## [601] 9.478965e-01 9.112817e-01 4.784785e-01 6.378720e-01 7.213602e-01
## [606] 7.785942e-01 5.183321e-01 4.088111e-01 7.216654e-01 5.112628e-01
## [611] 1.664093e-01 7.442091e-01 7.177763e-01 7.810933e-01 1.541778e-01
## [616] 3.186915e-01 5.596288e-01 8.433021e-01 3.325877e-02 4.342734e-01
## [621] 8.095645e-01 4.872840e-01 6.856618e-01 5.802561e-01 5.445898e-01
## [626] 8.924191e-01 9.607235e-01 8.464082e-02 6.970038e-01 7.129752e-02
## [631] 6.025369e-01 5.666645e-02 3.464168e-01 8.854866e-01 3.252165e-01
## [636] 5.248964e-01 2.720931e-01 2.054297e-01 2.960741e-01 7.928350e-01
## [641] 9.389982e-01 3.841338e-01 5.231822e-01 5.273940e-01 8.352002e-01
## [646] 9.503047e-01 1.570067e-01 8.707817e-01 5.011961e-01 2.380964e-01
## [651] 1.532033e-01 2.784405e-01 6.023328e-01 2.055761e-01 3.653850e-01
## [656] 4.980906e-01 3.333706e-01 1.307740e-01 5.914516e-01 9.606333e-01
## [661] 7.319009e-01 5.883894e-01 1.460408e-01 5.367876e-01 2.747586e-01
## [666] 8.705515e-01 3.920157e-01 9.908860e-01 6.048773e-02 8.034167e-01
## [671] 7.275712e-01 5.884055e-01 9.237100e-01 4.044306e-01 2.708447e-01
## [676] 9.459045e-01 7.554368e-01 6.879219e-01 6.790765e-01 6.996228e-01
## [681] 4.921773e-01 8.886911e-01 7.897387e-03 2.147805e-01 6.715735e-01
## [686] 5.234068e-01 3.696714e-01 4.071095e-01 5.821847e-01 6.397265e-01
## [691] 2.395381e-01 7.420161e-01 8.568353e-01 2.952620e-01 5.931578e-01
## [696] 3.203528e-01 7.513739e-01 5.680876e-01 1.555267e-01 4.276966e-01
## [701] 3.409742e-01 1.646967e-01 7.654189e-02 7.537501e-01 2.707023e-01
## [706] 7.019607e-02 4.346656e-01 7.435392e-01 3.803657e-01 6.338144e-01
## [711] 8.569427e-01 4.787640e-01 4.160601e-01 6.365494e-01 8.783125e-01
## [716] 2.478456e-02 3.756689e-01 9.126529e-01 6.673236e-01 3.780742e-01
## [721] 2.191435e-02 8.276280e-01 4.297314e-01 5.665875e-01 7.431705e-01
## [726] 5.832351e-01 3.418806e-01 9.181565e-01 3.340268e-01 8.094687e-01
## [731] 8.628083e-01 6.197697e-01 9.033538e-01 7.901120e-01 4.940301e-01
## [736] 3.252066e-01 4.843155e-02 8.392686e-01 3.342548e-01 8.118339e-01
## [741] 3.582037e-02 8.490484e-02 4.415889e-01 9.393778e-01 7.054049e-01
## [746] 6.017652e-01 8.062309e-01 5.716962e-01 3.479546e-01 1.168473e-01
## [751] 3.355924e-01 3.822227e-01 2.696193e-01 7.951709e-01 6.954508e-01
## [756] 1.043239e-01 8.202302e-01 3.339785e-01 4.782370e-01 9.774427e-01
## [761] 1.383670e-01 1.145857e-01 1.683493e-01 3.884144e-01 1.525306e-01
## [766] 8.024759e-01 3.150374e-01 1.708818e-01 6.335455e-01 8.755750e-01
## [771] 8.788644e-01 6.648476e-01 8.582580e-01 9.731339e-01 1.465186e-01
## [776] 5.975990e-01 7.003408e-01 1.502774e-01 4.111686e-02 7.521634e-01
## [781] 6.777872e-01 4.656807e-01 8.712721e-01 1.736321e-01 3.966199e-01
## [786] 2.373199e-01 6.703909e-01 4.382607e-01 2.815670e-01 5.198245e-01
## [791] 4.500341e-01 5.953591e-01 5.774900e-01 1.915374e-02 5.701289e-01
## [796] 6.942351e-01 4.231544e-01 8.810686e-02 6.305628e-03 3.789689e-01
## [801] 2.064126e-01 7.437602e-01 4.830424e-02 6.940481e-01 3.980159e-01
## [806] 6.244188e-01 3.203920e-01 6.434991e-01 3.445591e-01 2.137845e-01
## [811] 5.901669e-01 9.480989e-01 6.806198e-01 1.964928e-01 9.058425e-01
## [816] 9.229914e-01 7.178285e-01 2.972734e-01 6.865350e-01 7.293308e-01
## [821] 5.259846e-01 8.045805e-01 9.063170e-01 8.280307e-01 8.685381e-01
## [826] 2.034445e-01 4.694860e-01 5.575934e-01 5.931653e-01 6.843830e-01
## [831] 8.518877e-01 4.735307e-01 8.001589e-01 4.702900e-01 3.668289e-01
## [836] 1.981691e-01 8.223886e-01 5.190996e-01 4.548548e-01 2.963259e-01
## [841] 9.495547e-01 9.534361e-01 3.123150e-01 7.585515e-01 4.173447e-02
## [846] 5.648072e-01 8.103133e-01 6.355814e-01 1.493360e-01 5.968443e-01
## [851] 2.688214e-01 2.777440e-01 9.817018e-01 7.258406e-01 5.061742e-02
## [856] 3.535774e-01 5.346878e-01 9.143274e-01 4.966553e-01 4.827973e-02
## [861] 5.108321e-01 3.749254e-01 2.462751e-02 7.943781e-01 4.233031e-01
## [866] 2.646600e-01 4.013761e-01 8.266212e-01 8.304557e-01 9.286837e-01
## [871] 4.914450e-01 5.404059e-01 9.341207e-01 9.387683e-01 2.843042e-01
## [876] 6.494706e-01 5.973622e-01 2.704677e-01 7.451151e-01 4.507812e-01
## [881] 6.590495e-01 9.790256e-01 5.445354e-01 2.695137e-01 6.942979e-01
## [886] 4.518315e-01 3.603045e-01 2.563461e-01 8.244200e-02 5.576960e-01
## [891] 5.436161e-01 8.908526e-01 3.442724e-01 3.747487e-01 4.921379e-01
## [896] 9.868779e-01 5.824403e-01 9.735498e-01 2.246427e-01 7.273746e-01
## [901] 9.745670e-02 3.325783e-01 8.884770e-01 6.748801e-01 1.380391e-01
## [906] 2.843195e-01 3.857804e-01 5.298787e-03 7.777601e-01 2.557183e-01
## [911] 7.757106e-01 3.269052e-01 4.209785e-02 1.053073e-01 2.867753e-01
## [916] 9.316726e-01 7.681227e-01 5.318627e-02 3.544376e-01 5.730234e-02
## [921] 4.136462e-02 7.117066e-01 7.875811e-01 3.288080e-01 8.925189e-01
## [926] 7.805549e-01 1.675484e-01 7.293990e-01 8.193844e-01 5.039317e-01
## [931] 2.859903e-01 3.751391e-02 8.341236e-01 9.797432e-01 1.823155e-01
## [936] 5.526054e-01 8.158086e-01 8.982437e-01 1.224571e-01 1.246576e-01
## [941] 3.482577e-01 7.476235e-01 5.315777e-01 7.862607e-01 5.918113e-01
## [946] 3.218044e-01 8.194836e-01 2.933954e-01 4.900591e-01 6.425393e-01
## [951] 1.537513e-02 1.729846e-01 1.407576e-01 5.113641e-01 5.511314e-02
## [956] 3.665409e-01 2.945542e-01 4.261331e-01 8.718435e-01 7.574763e-01
## [961] 1.366512e-01 2.896404e-01 2.322764e-01 2.138440e-01 4.644431e-01
## [966] 1.324033e-01 2.396143e-01 4.221037e-01 3.694090e-01 7.438046e-01
## [971] 1.914406e-01 2.787928e-02 7.608173e-01 4.100203e-01 8.884061e-02
## [976] 4.251041e-01 1.995386e-01 9.255478e-01 1.156056e-01 3.992775e-01
## [981] 5.231715e-01 1.381811e-02 1.380220e-02 2.459784e-01 6.225481e-01
## [986] 1.890305e-02 4.692894e-01 7.046586e-02 4.575500e-01 3.983723e-01
## [991] 8.298402e-01 2.181346e-01 5.763028e-01 7.140385e-01 3.544772e-01
## [996] 9.703545e-01 9.830463e-01 6.292399e-01 4.015046e-02 1.026913e-01dat2<- data.frame(v2)
## generando graficos ...
ggplot(dat2, aes(v2))+geom_histogram(binwidth = 0.1,col="black",fill="blue",alpha=0.4,) + labs(y="Conteo",x="Valor de datos muestr2/m",title = "Valores generados con operador congrencial multiplicativo")+ theme_bw()
Probar que provenga de una distribucion uniforme [0,1] DECISION DE HIPOTESIS A PROVAR \[H_0: U\sim Uniforme(0,1)\] \[H_1: U\nsim Uniforme(0,1)\]
ks.test(v2,punif,0,1)##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: v2
## D = 0.02766, p-value = 0.4286
## alternative hypothesis: two-sidedDe acuerdo a los resultados, p-valor = 0.4286, si alpha es mayor que p-valor se rechaza Ho. Note que p-valor es mayor que alpha Por lo tanto NO RECHAZA. es decir, la muestra simulada proviene de una distribución uniforme ########################################################################################### ##########################################################################################
Prueba de independencia de la muestra generada (autocorrelacion) autocorrelacion (ACF) mide la autocorrelacion de una seriel temporal en diferentes intervalos de tiempo.
prueIND2<- acf(v2, type= "correlation");prueIND2 # Ver si hay independencia en la muestra generada
##
## Autocorrelations of series 'v2', by lag
##
## 0 1 2 3 4 5 6 7 8 9 10
## 1.000 0.003 -0.021 0.027 0.001 -0.017 0.025 -0.016 0.041 0.045 -0.036
## 11 12 13 14 15 16 17 18 19 20 21
## 0.028 0.019 0.011 -0.020 0.008 -0.045 0.022 -0.029 0.010 0.036 -0.004
## 22 23 24 25 26 27 28 29 30
## -0.027 -0.031 -0.016 -0.025 0.044 0.023 0.009 -0.049 -0.051No hay correlación en los datos de la muestra generada de una uniforme Como en el gráfico se ve que las barras salen del rango, Por lo tanto se concluye , que la muesta es independiente. ################################################ Con el estadístico Ljung-Box, se puede probar \(H_{0}\): Muestra aleatoria \(H_{1}\): Muestra no aleatoria
Se rechaza \(H_{0}\) si \(p-valor <\alpha\)
Box.test(v2, lag = 10, type = "Ljung")##
## Box-Ljung test
##
## data: v2
## X-squared = 7.4561, df = 10, p-value = 0.6818De acuerdo a los resultados, p-valor = 0.6818, Note que \(p-valor > \alpha\), llegamos a conclusion ,que No se rechaza \(H0\) Por lo tanto La muestra generada es aleatoria
#######################################################################################3
- \(c=1\), \(a=5\) y \(m=512\)
rm(list=ls())
n <- 1000 # numero de numeros aleatorios a generar (1000)
a <- 5 #valor de operacion
m <- 512 #valor del modulo
c <- 0
muestr3 <-45183 # Fijar un valor a la semilla asignamos el valor de muestr
# Enseguida se utiliza el ciclo for para generar los valores aleatorios en n muestra
#iniciando en la posicion 2,tomara el valor de 2-1, pues en este caso la semilla inicial 45183, sera el primer posicion.
for(i in 2:n)
{
muestr3[i]<-(a*muestr3[i-1]+c)%%m
}
muestr3## [1] 45183 123 103 3 15 75 375 339 159 283 391 419
## [13] 47 235 151 243 191 443 167 323 79 395 439 147
## [25] 223 91 455 227 111 43 215 51 255 251 231 131
## [37] 143 203 503 467 287 411 7 35 175 363 279 371
## [49] 319 59 295 451 207 11 55 275 351 219 71 355
## [61] 239 171 343 179 383 379 359 259 271 331 119 83
## [73] 415 27 135 163 303 491 407 499 447 187 423 67
## [85] 335 139 183 403 479 347 199 483 367 299 471 307
## [97] 511 507 487 387 399 459 247 211 31 155 263 291
## [109] 431 107 23 115 63 315 39 195 463 267 311 19
## [121] 95 475 327 99 495 427 87 435 127 123 103 3
## [133] 15 75 375 339 159 283 391 419 47 235 151 243
## [145] 191 443 167 323 79 395 439 147 223 91 455 227
## [157] 111 43 215 51 255 251 231 131 143 203 503 467
## [169] 287 411 7 35 175 363 279 371 319 59 295 451
## [181] 207 11 55 275 351 219 71 355 239 171 343 179
## [193] 383 379 359 259 271 331 119 83 415 27 135 163
## [205] 303 491 407 499 447 187 423 67 335 139 183 403
## [217] 479 347 199 483 367 299 471 307 511 507 487 387
## [229] 399 459 247 211 31 155 263 291 431 107 23 115
## [241] 63 315 39 195 463 267 311 19 95 475 327 99
## [253] 495 427 87 435 127 123 103 3 15 75 375 339
## [265] 159 283 391 419 47 235 151 243 191 443 167 323
## [277] 79 395 439 147 223 91 455 227 111 43 215 51
## [289] 255 251 231 131 143 203 503 467 287 411 7 35
## [301] 175 363 279 371 319 59 295 451 207 11 55 275
## [313] 351 219 71 355 239 171 343 179 383 379 359 259
## [325] 271 331 119 83 415 27 135 163 303 491 407 499
## [337] 447 187 423 67 335 139 183 403 479 347 199 483
## [349] 367 299 471 307 511 507 487 387 399 459 247 211
## [361] 31 155 263 291 431 107 23 115 63 315 39 195
## [373] 463 267 311 19 95 475 327 99 495 427 87 435
## [385] 127 123 103 3 15 75 375 339 159 283 391 419
## [397] 47 235 151 243 191 443 167 323 79 395 439 147
## [409] 223 91 455 227 111 43 215 51 255 251 231 131
## [421] 143 203 503 467 287 411 7 35 175 363 279 371
## [433] 319 59 295 451 207 11 55 275 351 219 71 355
## [445] 239 171 343 179 383 379 359 259 271 331 119 83
## [457] 415 27 135 163 303 491 407 499 447 187 423 67
## [469] 335 139 183 403 479 347 199 483 367 299 471 307
## [481] 511 507 487 387 399 459 247 211 31 155 263 291
## [493] 431 107 23 115 63 315 39 195 463 267 311 19
## [505] 95 475 327 99 495 427 87 435 127 123 103 3
## [517] 15 75 375 339 159 283 391 419 47 235 151 243
## [529] 191 443 167 323 79 395 439 147 223 91 455 227
## [541] 111 43 215 51 255 251 231 131 143 203 503 467
## [553] 287 411 7 35 175 363 279 371 319 59 295 451
## [565] 207 11 55 275 351 219 71 355 239 171 343 179
## [577] 383 379 359 259 271 331 119 83 415 27 135 163
## [589] 303 491 407 499 447 187 423 67 335 139 183 403
## [601] 479 347 199 483 367 299 471 307 511 507 487 387
## [613] 399 459 247 211 31 155 263 291 431 107 23 115
## [625] 63 315 39 195 463 267 311 19 95 475 327 99
## [637] 495 427 87 435 127 123 103 3 15 75 375 339
## [649] 159 283 391 419 47 235 151 243 191 443 167 323
## [661] 79 395 439 147 223 91 455 227 111 43 215 51
## [673] 255 251 231 131 143 203 503 467 287 411 7 35
## [685] 175 363 279 371 319 59 295 451 207 11 55 275
## [697] 351 219 71 355 239 171 343 179 383 379 359 259
## [709] 271 331 119 83 415 27 135 163 303 491 407 499
## [721] 447 187 423 67 335 139 183 403 479 347 199 483
## [733] 367 299 471 307 511 507 487 387 399 459 247 211
## [745] 31 155 263 291 431 107 23 115 63 315 39 195
## [757] 463 267 311 19 95 475 327 99 495 427 87 435
## [769] 127 123 103 3 15 75 375 339 159 283 391 419
## [781] 47 235 151 243 191 443 167 323 79 395 439 147
## [793] 223 91 455 227 111 43 215 51 255 251 231 131
## [805] 143 203 503 467 287 411 7 35 175 363 279 371
## [817] 319 59 295 451 207 11 55 275 351 219 71 355
## [829] 239 171 343 179 383 379 359 259 271 331 119 83
## [841] 415 27 135 163 303 491 407 499 447 187 423 67
## [853] 335 139 183 403 479 347 199 483 367 299 471 307
## [865] 511 507 487 387 399 459 247 211 31 155 263 291
## [877] 431 107 23 115 63 315 39 195 463 267 311 19
## [889] 95 475 327 99 495 427 87 435 127 123 103 3
## [901] 15 75 375 339 159 283 391 419 47 235 151 243
## [913] 191 443 167 323 79 395 439 147 223 91 455 227
## [925] 111 43 215 51 255 251 231 131 143 203 503 467
## [937] 287 411 7 35 175 363 279 371 319 59 295 451
## [949] 207 11 55 275 351 219 71 355 239 171 343 179
## [961] 383 379 359 259 271 331 119 83 415 27 135 163
## [973] 303 491 407 499 447 187 423 67 335 139 183 403
## [985] 479 347 199 483 367 299 471 307 511 507 487 387
## [997] 399 459 247 211#A aprtir de la Asignacion de la mestr
#podemos calcular
#los siguientes
# 1 generar la media de la muestr a partir de la muestra generada
mean(muestr3)## [1] 302.696# 1 Genrar la varianza de la muestr a partir de la muestra generada
var(muestr3)## [1] 2040014#las funciones de ggplot unicamente trabaja con data frame
## guardar en los resultados de muestr/m como dataframe
## en datos
v3 <- muestr3/m
v3## [1] 88.248046875 0.240234375 0.201171875 0.005859375 0.029296875
## [6] 0.146484375 0.732421875 0.662109375 0.310546875 0.552734375
## [11] 0.763671875 0.818359375 0.091796875 0.458984375 0.294921875
## [16] 0.474609375 0.373046875 0.865234375 0.326171875 0.630859375
## [21] 0.154296875 0.771484375 0.857421875 0.287109375 0.435546875
## [26] 0.177734375 0.888671875 0.443359375 0.216796875 0.083984375
## [31] 0.419921875 0.099609375 0.498046875 0.490234375 0.451171875
## [36] 0.255859375 0.279296875 0.396484375 0.982421875 0.912109375
## [41] 0.560546875 0.802734375 0.013671875 0.068359375 0.341796875
## [46] 0.708984375 0.544921875 0.724609375 0.623046875 0.115234375
## [51] 0.576171875 0.880859375 0.404296875 0.021484375 0.107421875
## [56] 0.537109375 0.685546875 0.427734375 0.138671875 0.693359375
## [61] 0.466796875 0.333984375 0.669921875 0.349609375 0.748046875
## [66] 0.740234375 0.701171875 0.505859375 0.529296875 0.646484375
## [71] 0.232421875 0.162109375 0.810546875 0.052734375 0.263671875
## [76] 0.318359375 0.591796875 0.958984375 0.794921875 0.974609375
## [81] 0.873046875 0.365234375 0.826171875 0.130859375 0.654296875
## [86] 0.271484375 0.357421875 0.787109375 0.935546875 0.677734375
## [91] 0.388671875 0.943359375 0.716796875 0.583984375 0.919921875
## [96] 0.599609375 0.998046875 0.990234375 0.951171875 0.755859375
## [101] 0.779296875 0.896484375 0.482421875 0.412109375 0.060546875
## [106] 0.302734375 0.513671875 0.568359375 0.841796875 0.208984375
## [111] 0.044921875 0.224609375 0.123046875 0.615234375 0.076171875
## [116] 0.380859375 0.904296875 0.521484375 0.607421875 0.037109375
## [121] 0.185546875 0.927734375 0.638671875 0.193359375 0.966796875
## [126] 0.833984375 0.169921875 0.849609375 0.248046875 0.240234375
## [131] 0.201171875 0.005859375 0.029296875 0.146484375 0.732421875
## [136] 0.662109375 0.310546875 0.552734375 0.763671875 0.818359375
## [141] 0.091796875 0.458984375 0.294921875 0.474609375 0.373046875
## [146] 0.865234375 0.326171875 0.630859375 0.154296875 0.771484375
## [151] 0.857421875 0.287109375 0.435546875 0.177734375 0.888671875
## [156] 0.443359375 0.216796875 0.083984375 0.419921875 0.099609375
## [161] 0.498046875 0.490234375 0.451171875 0.255859375 0.279296875
## [166] 0.396484375 0.982421875 0.912109375 0.560546875 0.802734375
## [171] 0.013671875 0.068359375 0.341796875 0.708984375 0.544921875
## [176] 0.724609375 0.623046875 0.115234375 0.576171875 0.880859375
## [181] 0.404296875 0.021484375 0.107421875 0.537109375 0.685546875
## [186] 0.427734375 0.138671875 0.693359375 0.466796875 0.333984375
## [191] 0.669921875 0.349609375 0.748046875 0.740234375 0.701171875
## [196] 0.505859375 0.529296875 0.646484375 0.232421875 0.162109375
## [201] 0.810546875 0.052734375 0.263671875 0.318359375 0.591796875
## [206] 0.958984375 0.794921875 0.974609375 0.873046875 0.365234375
## [211] 0.826171875 0.130859375 0.654296875 0.271484375 0.357421875
## [216] 0.787109375 0.935546875 0.677734375 0.388671875 0.943359375
## [221] 0.716796875 0.583984375 0.919921875 0.599609375 0.998046875
## [226] 0.990234375 0.951171875 0.755859375 0.779296875 0.896484375
## [231] 0.482421875 0.412109375 0.060546875 0.302734375 0.513671875
## [236] 0.568359375 0.841796875 0.208984375 0.044921875 0.224609375
## [241] 0.123046875 0.615234375 0.076171875 0.380859375 0.904296875
## [246] 0.521484375 0.607421875 0.037109375 0.185546875 0.927734375
## [251] 0.638671875 0.193359375 0.966796875 0.833984375 0.169921875
## [256] 0.849609375 0.248046875 0.240234375 0.201171875 0.005859375
## [261] 0.029296875 0.146484375 0.732421875 0.662109375 0.310546875
## [266] 0.552734375 0.763671875 0.818359375 0.091796875 0.458984375
## [271] 0.294921875 0.474609375 0.373046875 0.865234375 0.326171875
## [276] 0.630859375 0.154296875 0.771484375 0.857421875 0.287109375
## [281] 0.435546875 0.177734375 0.888671875 0.443359375 0.216796875
## [286] 0.083984375 0.419921875 0.099609375 0.498046875 0.490234375
## [291] 0.451171875 0.255859375 0.279296875 0.396484375 0.982421875
## [296] 0.912109375 0.560546875 0.802734375 0.013671875 0.068359375
## [301] 0.341796875 0.708984375 0.544921875 0.724609375 0.623046875
## [306] 0.115234375 0.576171875 0.880859375 0.404296875 0.021484375
## [311] 0.107421875 0.537109375 0.685546875 0.427734375 0.138671875
## [316] 0.693359375 0.466796875 0.333984375 0.669921875 0.349609375
## [321] 0.748046875 0.740234375 0.701171875 0.505859375 0.529296875
## [326] 0.646484375 0.232421875 0.162109375 0.810546875 0.052734375
## [331] 0.263671875 0.318359375 0.591796875 0.958984375 0.794921875
## [336] 0.974609375 0.873046875 0.365234375 0.826171875 0.130859375
## [341] 0.654296875 0.271484375 0.357421875 0.787109375 0.935546875
## [346] 0.677734375 0.388671875 0.943359375 0.716796875 0.583984375
## [351] 0.919921875 0.599609375 0.998046875 0.990234375 0.951171875
## [356] 0.755859375 0.779296875 0.896484375 0.482421875 0.412109375
## [361] 0.060546875 0.302734375 0.513671875 0.568359375 0.841796875
## [366] 0.208984375 0.044921875 0.224609375 0.123046875 0.615234375
## [371] 0.076171875 0.380859375 0.904296875 0.521484375 0.607421875
## [376] 0.037109375 0.185546875 0.927734375 0.638671875 0.193359375
## [381] 0.966796875 0.833984375 0.169921875 0.849609375 0.248046875
## [386] 0.240234375 0.201171875 0.005859375 0.029296875 0.146484375
## [391] 0.732421875 0.662109375 0.310546875 0.552734375 0.763671875
## [396] 0.818359375 0.091796875 0.458984375 0.294921875 0.474609375
## [401] 0.373046875 0.865234375 0.326171875 0.630859375 0.154296875
## [406] 0.771484375 0.857421875 0.287109375 0.435546875 0.177734375
## [411] 0.888671875 0.443359375 0.216796875 0.083984375 0.419921875
## [416] 0.099609375 0.498046875 0.490234375 0.451171875 0.255859375
## [421] 0.279296875 0.396484375 0.982421875 0.912109375 0.560546875
## [426] 0.802734375 0.013671875 0.068359375 0.341796875 0.708984375
## [431] 0.544921875 0.724609375 0.623046875 0.115234375 0.576171875
## [436] 0.880859375 0.404296875 0.021484375 0.107421875 0.537109375
## [441] 0.685546875 0.427734375 0.138671875 0.693359375 0.466796875
## [446] 0.333984375 0.669921875 0.349609375 0.748046875 0.740234375
## [451] 0.701171875 0.505859375 0.529296875 0.646484375 0.232421875
## [456] 0.162109375 0.810546875 0.052734375 0.263671875 0.318359375
## [461] 0.591796875 0.958984375 0.794921875 0.974609375 0.873046875
## [466] 0.365234375 0.826171875 0.130859375 0.654296875 0.271484375
## [471] 0.357421875 0.787109375 0.935546875 0.677734375 0.388671875
## [476] 0.943359375 0.716796875 0.583984375 0.919921875 0.599609375
## [481] 0.998046875 0.990234375 0.951171875 0.755859375 0.779296875
## [486] 0.896484375 0.482421875 0.412109375 0.060546875 0.302734375
## [491] 0.513671875 0.568359375 0.841796875 0.208984375 0.044921875
## [496] 0.224609375 0.123046875 0.615234375 0.076171875 0.380859375
## [501] 0.904296875 0.521484375 0.607421875 0.037109375 0.185546875
## [506] 0.927734375 0.638671875 0.193359375 0.966796875 0.833984375
## [511] 0.169921875 0.849609375 0.248046875 0.240234375 0.201171875
## [516] 0.005859375 0.029296875 0.146484375 0.732421875 0.662109375
## [521] 0.310546875 0.552734375 0.763671875 0.818359375 0.091796875
## [526] 0.458984375 0.294921875 0.474609375 0.373046875 0.865234375
## [531] 0.326171875 0.630859375 0.154296875 0.771484375 0.857421875
## [536] 0.287109375 0.435546875 0.177734375 0.888671875 0.443359375
## [541] 0.216796875 0.083984375 0.419921875 0.099609375 0.498046875
## [546] 0.490234375 0.451171875 0.255859375 0.279296875 0.396484375
## [551] 0.982421875 0.912109375 0.560546875 0.802734375 0.013671875
## [556] 0.068359375 0.341796875 0.708984375 0.544921875 0.724609375
## [561] 0.623046875 0.115234375 0.576171875 0.880859375 0.404296875
## [566] 0.021484375 0.107421875 0.537109375 0.685546875 0.427734375
## [571] 0.138671875 0.693359375 0.466796875 0.333984375 0.669921875
## [576] 0.349609375 0.748046875 0.740234375 0.701171875 0.505859375
## [581] 0.529296875 0.646484375 0.232421875 0.162109375 0.810546875
## [586] 0.052734375 0.263671875 0.318359375 0.591796875 0.958984375
## [591] 0.794921875 0.974609375 0.873046875 0.365234375 0.826171875
## [596] 0.130859375 0.654296875 0.271484375 0.357421875 0.787109375
## [601] 0.935546875 0.677734375 0.388671875 0.943359375 0.716796875
## [606] 0.583984375 0.919921875 0.599609375 0.998046875 0.990234375
## [611] 0.951171875 0.755859375 0.779296875 0.896484375 0.482421875
## [616] 0.412109375 0.060546875 0.302734375 0.513671875 0.568359375
## [621] 0.841796875 0.208984375 0.044921875 0.224609375 0.123046875
## [626] 0.615234375 0.076171875 0.380859375 0.904296875 0.521484375
## [631] 0.607421875 0.037109375 0.185546875 0.927734375 0.638671875
## [636] 0.193359375 0.966796875 0.833984375 0.169921875 0.849609375
## [641] 0.248046875 0.240234375 0.201171875 0.005859375 0.029296875
## [646] 0.146484375 0.732421875 0.662109375 0.310546875 0.552734375
## [651] 0.763671875 0.818359375 0.091796875 0.458984375 0.294921875
## [656] 0.474609375 0.373046875 0.865234375 0.326171875 0.630859375
## [661] 0.154296875 0.771484375 0.857421875 0.287109375 0.435546875
## [666] 0.177734375 0.888671875 0.443359375 0.216796875 0.083984375
## [671] 0.419921875 0.099609375 0.498046875 0.490234375 0.451171875
## [676] 0.255859375 0.279296875 0.396484375 0.982421875 0.912109375
## [681] 0.560546875 0.802734375 0.013671875 0.068359375 0.341796875
## [686] 0.708984375 0.544921875 0.724609375 0.623046875 0.115234375
## [691] 0.576171875 0.880859375 0.404296875 0.021484375 0.107421875
## [696] 0.537109375 0.685546875 0.427734375 0.138671875 0.693359375
## [701] 0.466796875 0.333984375 0.669921875 0.349609375 0.748046875
## [706] 0.740234375 0.701171875 0.505859375 0.529296875 0.646484375
## [711] 0.232421875 0.162109375 0.810546875 0.052734375 0.263671875
## [716] 0.318359375 0.591796875 0.958984375 0.794921875 0.974609375
## [721] 0.873046875 0.365234375 0.826171875 0.130859375 0.654296875
## [726] 0.271484375 0.357421875 0.787109375 0.935546875 0.677734375
## [731] 0.388671875 0.943359375 0.716796875 0.583984375 0.919921875
## [736] 0.599609375 0.998046875 0.990234375 0.951171875 0.755859375
## [741] 0.779296875 0.896484375 0.482421875 0.412109375 0.060546875
## [746] 0.302734375 0.513671875 0.568359375 0.841796875 0.208984375
## [751] 0.044921875 0.224609375 0.123046875 0.615234375 0.076171875
## [756] 0.380859375 0.904296875 0.521484375 0.607421875 0.037109375
## [761] 0.185546875 0.927734375 0.638671875 0.193359375 0.966796875
## [766] 0.833984375 0.169921875 0.849609375 0.248046875 0.240234375
## [771] 0.201171875 0.005859375 0.029296875 0.146484375 0.732421875
## [776] 0.662109375 0.310546875 0.552734375 0.763671875 0.818359375
## [781] 0.091796875 0.458984375 0.294921875 0.474609375 0.373046875
## [786] 0.865234375 0.326171875 0.630859375 0.154296875 0.771484375
## [791] 0.857421875 0.287109375 0.435546875 0.177734375 0.888671875
## [796] 0.443359375 0.216796875 0.083984375 0.419921875 0.099609375
## [801] 0.498046875 0.490234375 0.451171875 0.255859375 0.279296875
## [806] 0.396484375 0.982421875 0.912109375 0.560546875 0.802734375
## [811] 0.013671875 0.068359375 0.341796875 0.708984375 0.544921875
## [816] 0.724609375 0.623046875 0.115234375 0.576171875 0.880859375
## [821] 0.404296875 0.021484375 0.107421875 0.537109375 0.685546875
## [826] 0.427734375 0.138671875 0.693359375 0.466796875 0.333984375
## [831] 0.669921875 0.349609375 0.748046875 0.740234375 0.701171875
## [836] 0.505859375 0.529296875 0.646484375 0.232421875 0.162109375
## [841] 0.810546875 0.052734375 0.263671875 0.318359375 0.591796875
## [846] 0.958984375 0.794921875 0.974609375 0.873046875 0.365234375
## [851] 0.826171875 0.130859375 0.654296875 0.271484375 0.357421875
## [856] 0.787109375 0.935546875 0.677734375 0.388671875 0.943359375
## [861] 0.716796875 0.583984375 0.919921875 0.599609375 0.998046875
## [866] 0.990234375 0.951171875 0.755859375 0.779296875 0.896484375
## [871] 0.482421875 0.412109375 0.060546875 0.302734375 0.513671875
## [876] 0.568359375 0.841796875 0.208984375 0.044921875 0.224609375
## [881] 0.123046875 0.615234375 0.076171875 0.380859375 0.904296875
## [886] 0.521484375 0.607421875 0.037109375 0.185546875 0.927734375
## [891] 0.638671875 0.193359375 0.966796875 0.833984375 0.169921875
## [896] 0.849609375 0.248046875 0.240234375 0.201171875 0.005859375
## [901] 0.029296875 0.146484375 0.732421875 0.662109375 0.310546875
## [906] 0.552734375 0.763671875 0.818359375 0.091796875 0.458984375
## [911] 0.294921875 0.474609375 0.373046875 0.865234375 0.326171875
## [916] 0.630859375 0.154296875 0.771484375 0.857421875 0.287109375
## [921] 0.435546875 0.177734375 0.888671875 0.443359375 0.216796875
## [926] 0.083984375 0.419921875 0.099609375 0.498046875 0.490234375
## [931] 0.451171875 0.255859375 0.279296875 0.396484375 0.982421875
## [936] 0.912109375 0.560546875 0.802734375 0.013671875 0.068359375
## [941] 0.341796875 0.708984375 0.544921875 0.724609375 0.623046875
## [946] 0.115234375 0.576171875 0.880859375 0.404296875 0.021484375
## [951] 0.107421875 0.537109375 0.685546875 0.427734375 0.138671875
## [956] 0.693359375 0.466796875 0.333984375 0.669921875 0.349609375
## [961] 0.748046875 0.740234375 0.701171875 0.505859375 0.529296875
## [966] 0.646484375 0.232421875 0.162109375 0.810546875 0.052734375
## [971] 0.263671875 0.318359375 0.591796875 0.958984375 0.794921875
## [976] 0.974609375 0.873046875 0.365234375 0.826171875 0.130859375
## [981] 0.654296875 0.271484375 0.357421875 0.787109375 0.935546875
## [986] 0.677734375 0.388671875 0.943359375 0.716796875 0.583984375
## [991] 0.919921875 0.599609375 0.998046875 0.990234375 0.951171875
## [996] 0.755859375 0.779296875 0.896484375 0.482421875 0.412109375dat3<- data.frame(v3)
## generando graficos ...
ggplot(dat3, aes(v3))+geom_histogram(binwidth = 0.1,col="pink",fill="blue",alpha=0.1,) + labs(y="Conteo",x="Valor de datos muestr3/m",title = "Valores generados con operador congrencial multiplicativo")+ theme_bw()
Probar que provenga de una distribucion uniforme [0,1] DECISION DE HIPOTESIS A PROVAR \[H_0: U\sim Uniforme(0,1)\] \[H_1: U\nsim Uniforme(0,1)\]
ks.test(v3,punif,0,1)##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: v3
## D = 0.010859, p-value = 0.9998
## alternative hypothesis: two-sidedDe acuerdo a los resultados, p-valor = 0.9998, si alpha es mayor que p-valor se rechaza Ho. Note que p-valor es mayor que alpha Por lo tanto NO RECHAZA. es decir, la muestra simulada proviene de una distribución uniforme ########################################################################################### ##########################################################################################
Prueba de independencia de la muestra generada (autocorrelacion) autocorrelacion (ACF) mide la autocorrelacion de una seriel temporal en diferentes intervalos de tiempo.
prueIND3<- acf(v3, type= "correlation");prueIND3 # Ver si hay independencia en la muestra generada
##
## Autocorrelations of series 'v3', by lag
##
## 0 1 2 3 4 5 6 7 8 9 10
## 1.000 -0.001 -0.003 -0.005 -0.005 -0.004 0.002 0.002 -0.002 0.001 0.004
## 11 12 13 14 15 16 17 18 19 20 21
## 0.004 -0.004 -0.001 -0.003 -0.001 -0.002 0.005 -0.002 0.002 -0.003 0.004
## 22 23 24 25 26 27 28 29 30
## 0.004 -0.003 -0.001 -0.004 0.004 0.000 -0.002 -0.003 -0.001No hay correlación en los datos de la muestra generada de una uniforme Como en el gráfico se ve que las barras salen del rango, Por lo tanto se concluye , que la muesta es independiente. ################################################ Con el estadístico Ljung-Box, se puede probar \(H_{0}\): Muestra aleatoria \(H_{1}\): Muestra no aleatoria
Se rechaza \(H_{0}\) si \(p-valor <\alpha\)
Box.test(v3, lag = 10, type = "Ljung")##
## Box-Ljung test
##
## data: v3
## X-squared = 0.098741, df = 10, p-value = 1De acuerdo a los resultados, p-valor = 1, Note que \(p-valor > \alpha\), llegamos a conclusion ,que No se rechaza \(H0\) Por lo tanto La muestra generada es aleatoria
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