##Generando los números Pseudoalaeatorios

set.seed(3009)
num_aleat <- runif(100)
num_aleat
##   [1] 0.2693463224 0.4057150499 0.4789595187 0.2005149745 0.4679950266
##   [6] 0.9924790736 0.1712180756 0.3937174589 0.7092818038 0.5609353920
##  [11] 0.8682629522 0.9212334319 0.8751491096 0.3152880401 0.5748982185
##  [16] 0.9325285542 0.2493617632 0.5899179131 0.0457652817 0.0786426552
##  [21] 0.6905312026 0.3372408927 0.9690482512 0.6124100294 0.9852369330
##  [26] 0.8383921152 0.2948202908 0.9483264750 0.2560473441 0.3852935357
##  [31] 0.9416435095 0.9971495299 0.6427476760 0.4381843274 0.9889746860
##  [36] 0.5680761652 0.1697438646 0.7689988425 0.2154922828 0.1471966370
##  [41] 0.1664867220 0.8153620965 0.7942233777 0.3674672716 0.2535557465
##  [46] 0.5501284762 0.3520138548 0.4544020810 0.1670556171 0.1603428181
##  [51] 0.2262774182 0.8016169057 0.6030836308 0.9050466034 0.3624372736
##  [56] 0.1908530786 0.8342494743 0.2882433748 0.2389226626 0.2539414112
##  [61] 0.8878831652 0.9302236815 0.0001397894 0.6366907707 0.4309501559
##  [66] 0.5130254738 0.9552188928 0.9721634332 0.0455631623 0.6700149551
##  [71] 0.7631773711 0.7592177724 0.4990691915 0.3085287502 0.7839094084
##  [76] 0.9558199723 0.5680055534 0.9943322751 0.3677756281 0.9702452854
##  [81] 0.4848087020 0.0408915011 0.9666668135 0.6162433978 0.2438061498
##  [86] 0.7746479886 0.8804058437 0.5321420769 0.6400519614 0.2938680288
##  [91] 0.6650891975 0.2839593720 0.9162857858 0.0581468043 0.9064241699
##  [96] 0.9197621278 0.0245081070 0.4192247139 0.5373052941 0.0382239423

Prueba de unifromidad chi cuadrada

histo <- hist(num_aleat, breaks=6)

Prueba de Corrida

diff(num_aleat)
##  [1]  0.136368728  0.073244469 -0.278444544  0.267480052  0.524484047
##  [6] -0.821260998  0.222499383  0.315564345 -0.148346412  0.307327560
## [11]  0.052970480 -0.046084322 -0.559861070  0.259610178  0.357630336
## [16] -0.683166791  0.340556150 -0.544152631  0.032877374  0.611888547
## [21] -0.353290310  0.631807358 -0.356638222  0.372826904 -0.146844818
## [26] -0.543571824  0.653506184 -0.692279131  0.129246192  0.556349974
## [31]  0.055506020 -0.354401854 -0.204563349  0.550790359 -0.420898521
## [36] -0.398332301  0.599254978 -0.553506560 -0.068295646  0.019290085
## [41]  0.648875375 -0.021138719 -0.426756106 -0.113911525  0.296572730
## [46] -0.198114621  0.102388226 -0.287346464 -0.006712799  0.065934600
## [51]  0.575339488 -0.198533275  0.301962973 -0.542609330 -0.171584195
## [56]  0.643396396 -0.546006100 -0.049320712  0.015018749  0.633941754
## [61]  0.042340516 -0.930083892  0.636550981 -0.205740615  0.082075318
## [66]  0.442193419  0.016944540 -0.926600271  0.624451793  0.093162416
## [71] -0.003959599 -0.260148581 -0.190540441  0.475380658  0.171910564
## [76] -0.387814419  0.426326722 -0.626556647  0.602469657 -0.485436583
## [81] -0.443917201  0.925775312 -0.350423416 -0.372437248  0.530841839
## [86]  0.105757855 -0.348263767  0.107909885 -0.346183933  0.371221169
## [91] -0.381129825  0.632326414 -0.858138982  0.848277366  0.013337958
## [96] -0.895254021  0.394716607  0.118080580 -0.499081352
S<-ifelse(diff(num_aleat) > 0, 1, 0) # secuencia de ceros y unos
S<-ifelse(diff(num_aleat) > 0, 1, 0) # secuencia de ceros y unos
cambios <- abs(diff(S))

Contar las corridas

corridas <- sum(cambios) + 1
corridas
## [1] 66
mu = (2*length(num_aleat)-1)/3 # media esperada de corrida 
mu
## [1] 66.33333
varianza <- (16*length(num_aleat)-29)/90
Z <- (corridas-mu)/sqrt(varianza) # valor de la estadística z
Z
## [1] -0.07978328
ifelse(Z<1.96,"Los u_i son independientes","Los u_i son dependeientes")
## [1] "Los u_i son independientes"

Prueba Run Test

library(DescTools)
RunsTest(S)
## 
##  Runs Test for Randomness
## 
## data:  S
## z = 3.064, runs = 66, m = 47, n = 52, p-value = 0.002184
## alternative hypothesis: true number of runs is not equal the expected number

Prueba de Poker

library(randtoolbox)
## Cargando paquete requerido: rngWELL
## This is randtoolbox. For an overview, type 'help("randtoolbox")'.
poker.test(num_aleat,nbcard=5)
## 
##           Poker test
## 
## chisq stat = 0.81, df = 4, p-value = 0.94
## 
##       (sample size : 100)
## 
##  observed number  0 1 11 7 1 
##  expected number  0.032 1.9 9.6 7.7 0.77

Informe

Generación de números pseudoaleatorios:Se generaron 100 números uniformes en [0,1]con semilla 3009. Esto garantiza que los resultados sean reproducibles.

Prueba de uniformidad (Chi-Cuadrado)

Secomparan las frecuencias observadas vs. esperadas en intervalos.<𝐻0H.:Los números son uniformes.Con 𝑝 >0.05 p>0.05, no se rechaza la uniformidad.

Prueba de Corridas (manual)

Se analizó la secuencia de aumentos y descensos.𝐻0H0.Los números son independientes. Si ∣𝑍∣<1.96∣Z∣<1.96, no se rechaza la independencia.

Prueba de Corridas con RunsTest() Valida automáticamente la independencia.Si 𝑝>0.05p>0.05, los números se consideran independientes.

Prueba de Póker: Se agrupan dígitos como “manos de póker” y se comparan patrones esperados.𝐻0H La secuencia es aleatoria.Si 𝑝>0.05 p>0.05, no hay evidencia contra la aleatoriedad.