METODOS DE GENERACION ALEATORIA.
OCTAVIO HERNANDEZ SATURNINO
2023-09-25
n<-1000
u<-runif(n)
x<-u^(1/3) # es el vector de longitud n, que contiene la muestra x1; x2; :::; xn
ks.test(x, "pbeta", 3,1)##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: x
## D = 0.032801, p-value = 0.2322
## alternative hypothesis: two-sidedhist(x,prob=TRUE,col = "green") #
curve(dbeta(x,3,1),xlab = "x",col="red",lwd=2, main="distribucion betha", add=TRUE)
# densidad de la curva.n<-1000
u<-runif(n)
a<-3
b<-1
x<-u^(1/3)
x## [1] 0.9342793 0.7476675 0.4971597 0.8904995 0.5989390 0.7440874 0.7623170
## [8] 0.8235375 0.6507386 0.2417467 0.8317038 0.7923888 0.9659029 0.8894414
## [15] 0.6174283 0.4265987 0.6014989 0.4800530 0.3474821 0.7553916 0.6777937
## [22] 0.7813031 0.9904279 0.9509672 0.6002818 0.9006831 0.9321281 0.7277517
## [29] 0.8063339 0.7398005 0.5100665 0.5140712 0.6642750 0.8509514 0.5120140
## [36] 0.9389996 0.9062564 0.4750478 0.9824463 0.8926923 0.9172275 0.7284941
## [43] 0.9863776 0.9776152 0.3327601 0.9930855 0.4371135 0.8925683 0.8681754
## [50] 0.8280393 0.7606866 0.9623832 0.9224832 0.8730676 0.3329314 0.9502229
## [57] 0.8312724 0.5786676 0.8146927 0.1934783 0.4548292 0.9197508 0.5266959
## [64] 0.8203934 0.8430077 0.5653599 0.3679090 0.8877112 0.8117615 0.2918880
## [71] 0.8425239 0.9789814 0.8990240 0.8984011 0.2248239 0.7428485 0.8699282
## [78] 0.5199732 0.9318076 0.7125289 0.4086687 0.9354166 0.9399419 0.9467048
## [85] 0.8009445 0.7569846 0.9683867 0.8190759 0.9433079 0.7701316 0.9449664
## [92] 0.8895027 0.6049954 0.9171447 0.4281273 0.9862682 0.7211327 0.8928369
## [99] 0.9628219 0.6388148 0.9976522 0.8808629 0.3283067 0.8695687 0.8461206
## [106] 0.9354865 0.9254686 0.8090431 0.9662337 0.7268909 0.4486363 0.8776202
## [113] 0.8520585 0.7454323 0.7612083 0.8515470 0.9615556 0.7385425 0.8533168
## [120] 0.8535090 0.9192735 0.8312359 0.9906900 0.9133366 0.5689554 0.9964588
## [127] 0.9927828 0.5606132 0.7556025 0.7939434 0.7946040 0.8177813 0.6843821
## [134] 0.7852570 0.2438056 0.9356310 0.8185275 0.8629337 0.4613257 0.5277608
## [141] 0.2652884 0.4328565 0.6250025 0.9912430 0.3702490 0.8288883 0.9657268
## [148] 0.9811187 0.3598951 0.8691539 0.5931867 0.9658234 0.4628385 0.5469955
## [155] 0.9060976 0.8481699 0.7983503 0.4244371 0.7878084 0.9423913 0.7936465
## [162] 0.6729637 0.8397150 0.5903730 0.5110323 0.8826629 0.7910176 0.2265155
## [169] 0.8467693 0.7409075 0.4391319 0.6472018 0.8677595 0.8668680 0.5404727
## [176] 0.6121545 0.7311771 0.4836013 0.8945268 0.9985283 0.9734704 0.4732670
## [183] 0.8599196 0.8352863 0.5490830 0.5835431 0.6820027 0.5469662 0.6595040
## [190] 0.7088969 0.7945357 0.4556610 0.9400547 0.5657779 0.7376857 0.9964093
## [197] 0.9808092 0.9568103 0.8876431 0.5368530 0.9672143 0.9056936 0.7513654
## [204] 0.9379941 0.3070068 0.7011995 0.8261285 0.7491247 0.9616794 0.9480432
## [211] 0.7767621 0.8953853 0.9977531 0.9213151 0.9663091 0.4700115 0.7090634
## [218] 0.5460370 0.4436864 0.7964325 0.6258880 0.9240195 0.7185366 0.8570793
## [225] 0.3392288 0.9423256 0.8489057 0.9046758 0.7187513 0.9797218 0.2185392
## [232] 0.7902896 0.4910783 0.6473598 0.2230808 0.8175107 0.8524878 0.5382332
## [239] 0.9661784 0.9981390 0.6909624 0.7191366 0.5616740 0.8939090 0.8584233
## [246] 0.8820715 0.7688755 0.9868872 0.2773943 0.9692399 0.2548649 0.8848526
## [253] 0.6081042 0.6663290 0.7775380 0.9973399 0.7713759 0.3045511 0.8744092
## [260] 0.6478356 0.6488115 0.9609304 0.8857677 0.5184999 0.9636359 0.8281634
## [267] 0.4129344 0.7025423 0.9861131 0.8687837 0.8689249 0.5771932 0.4323110
## [274] 0.8074150 0.7928933 0.6044937 0.2537193 0.1942184 0.6602480 0.3377147
## [281] 0.4194697 0.7607071 0.8607004 0.3979449 0.7501547 0.9540022 0.5151188
## [288] 0.9565659 0.9031634 0.9256934 0.8478785 0.8174408 0.5444859 0.5139460
## [295] 0.6667471 0.4544242 0.8002870 0.9742285 0.8635796 0.7000743 0.7223079
## [302] 0.5545481 0.5856282 0.7686017 0.7475701 0.8687305 0.9195341 0.7273045
## [309] 0.7631608 0.3855501 0.7714326 0.5211104 0.9446898 0.6810647 0.7838074
## [316] 0.5301492 0.9358096 0.9768405 0.7896042 0.8962101 0.9936035 0.8468186
## [323] 0.5674121 0.7412705 0.8521815 0.9517927 0.9125876 0.8946601 0.9648763
## [330] 0.7103866 0.6029878 0.8156335 0.6559337 0.9219131 0.8358248 0.9778600
## [337] 0.7317310 0.5778783 0.7192088 0.7409158 0.8964135 0.8133298 0.7048982
## [344] 0.8486393 0.6762101 0.9773119 0.9008913 0.6951710 0.4725241 0.2113969
## [351] 0.9407762 0.9036906 0.9147122 0.6897441 0.8973286 0.5438847 0.5859535
## [358] 0.5921936 0.7812117 0.7127274 0.8043706 0.4757351 0.5513331 0.5567189
## [365] 0.3479599 0.9792538 0.3481425 0.9911222 0.5853001 0.8338468 0.5759841
## [372] 0.9859240 0.9902415 0.7738292 0.9348360 0.9166949 0.6836606 0.7693130
## [379] 0.6963127 0.5522194 0.7174453 0.5445575 0.8604165 0.5996092 0.8719082
## [386] 0.6752877 0.4627599 0.4887002 0.9401725 0.5776963 0.1264397 0.7178505
## [393] 0.6425758 0.9441635 0.6386710 0.6284949 0.3354666 0.9863648 0.5856580
## [400] 0.9499492 0.8146885 0.5211963 0.9347076 0.8874246 0.7683522 0.9250694
## [407] 0.7412184 0.8984020 0.9672362 0.6381501 0.7870510 0.7840093 0.4227585
## [414] 0.9228357 0.6832567 0.3207011 0.8301882 0.8366831 0.7352690 0.5677751
## [421] 0.3261298 0.9280343 0.9127390 0.6369161 0.8253203 0.8742153 0.8038310
## [428] 0.7072825 0.6427058 0.3544634 0.6236969 0.6143754 0.6581279 0.8565325
## [435] 0.3404327 0.8427456 0.6320711 0.9512805 0.6222928 0.8677777 0.9811657
## [442] 0.6302485 0.8857780 0.8487441 0.8193724 0.6651334 0.8758749 0.7828047
## [449] 0.8991964 0.5089511 0.7591388 0.8938118 0.8934482 0.7182203 0.1938686
## [456] 0.1952601 0.3721823 0.8091500 0.9111006 0.6691125 0.8733678 0.7393790
## [463] 0.9534206 0.9630397 0.8939781 0.9152738 0.5316426 0.7909352 0.9024010
## [470] 0.6466436 0.7055491 0.7842242 0.6305191 0.4356057 0.9390881 0.4530137
## [477] 0.7497961 0.9218873 0.6424176 0.8614699 0.6383875 0.6147885 0.3962223
## [484] 0.6638196 0.9024659 0.4596018 0.9609732 0.7962416 0.5996639 0.8571282
## [491] 0.5980802 0.9310091 0.5531836 0.6995336 0.9535161 0.9337011 0.1045391
## [498] 0.6600163 0.7725732 0.8838683 0.7347409 0.9346637 0.7582220 0.6957868
## [505] 0.2074755 0.9752477 0.8755827 0.8087741 0.7193291 0.7051127 0.9385330
## [512] 0.9453111 0.6402840 0.6092366 0.8832866 0.5543130 0.7853103 0.4114363
## [519] 0.5163130 0.6418280 0.8300070 0.8807634 0.3201865 0.0681882 0.9012779
## [526] 0.8322956 0.7114760 0.6896467 0.8724280 0.8187557 0.7900673 0.5910722
## [533] 0.9066399 0.8879037 0.6644739 0.8708161 0.8350283 0.9118280 0.6932071
## [540] 0.8028101 0.6849589 0.6238969 0.8460689 0.7033579 0.4364221 0.3023967
## [547] 0.6795596 0.6395593 0.8938287 0.9369037 0.9410088 0.9448257 0.6067106
## [554] 0.8538682 0.8277367 0.7611626 0.6041769 0.6952469 0.4936700 0.8264448
## [561] 0.5986879 0.9443571 0.7919835 0.9355193 0.6330265 0.9774258 0.9756693
## [568] 0.8595368 0.8345234 0.5113427 0.8998817 0.6062911 0.7626165 0.3554366
## [575] 0.7189001 0.3125568 0.7946535 0.7470994 0.5239430 0.8093130 0.8811533
## [582] 0.9438161 0.9802498 0.9618163 0.3739207 0.7792046 0.9392665 0.5179577
## [589] 0.8918973 0.6410027 0.8645599 0.4317321 0.6256044 0.6497739 0.7540678
## [596] 0.7762668 0.8199457 0.9795567 0.7824704 0.9921083 0.8548360 0.7661791
## [603] 0.7941569 0.9710924 0.6513494 0.7210642 0.7852661 0.8081154 0.9076728
## [610] 0.4366467 0.4773209 0.8616404 0.4210331 0.4830771 0.7360148 0.9433595
## [617] 0.9360456 0.6743788 0.8723098 0.8066942 0.8912002 0.6110296 0.5993833
## [624] 0.8356075 0.7276301 0.1696088 0.6483931 0.7076164 0.7008211 0.8402410
## [631] 0.9394707 0.7618200 0.5467157 0.6838122 0.9947962 0.8163130 0.2680848
## [638] 0.9838598 0.8477340 0.7671598 0.8540462 0.9041837 0.6770850 0.8628370
## [645] 0.7055040 0.9744553 0.7570019 0.8486808 0.9220933 0.4704118 0.8111040
## [652] 0.1468461 0.7341057 0.9897892 0.4043847 0.7765464 0.7129880 0.8414612
## [659] 0.8258266 0.9611825 0.8644956 0.6589368 0.7021600 0.1924241 0.8149515
## [666] 0.9210588 0.9080784 0.9902412 0.7898027 0.8446606 0.7813501 0.9265944
## [673] 0.4388040 0.7478269 0.9569148 0.7133417 0.9278843 0.8050767 0.6975073
## [680] 0.8594867 0.7818790 0.9747660 0.9065345 0.8549295 0.9529274 0.2613569
## [687] 0.8627686 0.6961524 0.7790283 0.3237245 0.9693137 0.6568907 0.4490533
## [694] 0.9150204 0.6147627 0.7947559 0.6459807 0.6146885 0.7342401 0.9856433
## [701] 0.7880348 0.7141393 0.9115316 0.6236453 0.9864716 0.8257990 0.6404611
## [708] 0.8963494 0.8867805 0.8086342 0.7528259 0.9833891 0.7738430 0.7733192
## [715] 0.7008790 0.5068190 0.8383487 0.8199547 0.5943126 0.2362842 0.4144166
## [722] 0.8409765 0.7695323 0.8805080 0.6872217 0.7137801 0.7002342 0.8567159
## [729] 0.4511024 0.7730204 0.9420800 0.9672966 0.4968114 0.8262308 0.6197832
## [736] 0.9804004 0.4688914 0.4349061 0.8778823 0.6728745 0.7824938 0.9755480
## [743] 0.9683182 0.4726178 0.2422677 0.4188344 0.8778958 0.6564340 0.5162823
## [750] 0.9034214 0.9429597 0.6175655 0.7761392 0.3050661 0.4898144 0.7172117
## [757] 0.7021070 0.9398242 0.8342138 0.9989226 0.5217327 0.6403766 0.7962360
## [764] 0.6988229 0.7496622 0.6680695 0.6709761 0.9908129 0.5658634 0.9118194
## [771] 0.7878193 0.8168641 0.8974303 0.9028661 0.8110513 0.3685467 0.9939655
## [778] 0.8370108 0.6457209 0.6470432 0.3918154 0.8690946 0.6334615 0.6233552
## [785] 0.7365849 0.8701800 0.8928258 0.7227793 0.2769733 0.9105195 0.5962413
## [792] 0.2742485 0.5377859 0.9186353 0.9773868 0.6980194 0.6222136 0.7221471
## [799] 0.6016350 0.7309203 0.8628183 0.7228796 0.6781444 0.9487272 0.8268868
## [806] 0.9918172 0.6805203 0.9874938 0.8924203 0.2396195 0.5028221 0.4105651
## [813] 0.6625466 0.7933239 0.7135860 0.7761623 0.5531394 0.3551299 0.9615373
## [820] 0.9884628 0.8306397 0.9285220 0.6220744 0.9619016 0.5665907 0.7815522
## [827] 0.9415029 0.8788817 0.6053694 0.4043255 0.8720156 0.6734020 0.5448961
## [834] 0.3587548 0.6850387 0.9455163 0.8840895 0.8721429 0.7365144 0.4312200
## [841] 0.8880556 0.8759701 0.9153705 0.5991654 0.3460728 0.1327680 0.6553743
## [848] 0.4980569 0.8148661 0.9653679 0.6063847 0.9023490 0.9464883 0.6746800
## [855] 0.7871113 0.8456820 0.8074228 0.4873289 0.7582059 0.8673602 0.6831063
## [862] 0.9953299 0.9338495 0.6803436 0.9747149 0.7712679 0.9287420 0.7423446
## [869] 0.4581624 0.5803726 0.6572012 0.7442908 0.7769484 0.5261913 0.8698522
## [876] 0.9664846 0.8694201 0.6393387 0.8106885 0.9774772 0.4261683 0.8894785
## [883] 0.7883544 0.9152100 0.9640900 0.7405044 0.9423501 0.9637942 0.9280145
## [890] 0.7391357 0.9096061 0.3955496 0.5806439 0.8931658 0.4433689 0.7212868
## [897] 0.5792213 0.4838707 0.9868095 0.8134581 0.7527208 0.9623882 0.2284990
## [904] 0.9221687 0.8583761 0.5383977 0.8652671 0.9382876 0.7744208 0.3290009
## [911] 0.7466579 0.7862966 0.8525776 0.5255788 0.8567815 0.9673161 0.7579428
## [918] 0.9490559 0.7082760 0.6409705 0.5913993 0.7736021 0.4709542 0.1191974
## [925] 0.9314030 0.8216334 0.8527795 0.4991431 0.9114572 0.9293645 0.9101172
## [932] 0.4596922 0.7066623 0.8556295 0.9370655 0.8469353 0.6750187 0.9176223
## [939] 0.4480820 0.9151945 0.9907608 0.9536830 0.8405689 0.6936247 0.3983103
## [946] 0.8139226 0.8052043 0.4716045 0.8126773 0.6353558 0.4254832 0.7920913
## [953] 0.3429734 0.5363735 0.7851963 0.9325330 0.8434236 0.8772742 0.6140890
## [960] 0.3137814 0.7401512 0.9727120 0.6985213 0.8793467 0.8647414 0.8607118
## [967] 0.5884631 0.7890222 0.9317109 0.6869720 0.8533876 0.7346567 0.3299246
## [974] 0.7778243 0.7404717 0.8085867 0.9761609 0.8869263 0.5599434 0.8271372
## [981] 0.9592895 0.9468599 0.9146742 0.8790120 0.8223024 0.7335437 0.8920817
## [988] 0.8790566 0.9317763 0.6775550 0.9303031 0.6729191 0.8327427 0.5643182
## [995] 0.9435535 0.5740329 0.3151304 0.8490506 0.9822346 0.8674339# es el vector de longitud n, que contiene la muestra x1; x2; :::; xn
ks.test(x,"pbeta",a,b)##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: x
## D = 0.037899, p-value = 0.1131
## alternative hypothesis: two-sidedhist(x,prob=TRUE,col = "green") #
curve(dbeta(x,a,b),xlab = "x",col="red",lwd=2, main="distribucion betha", add=TRUE)
rm(list=ls())
y<-runif(1000,0,1)
lambda<-5
Cdf_Invs<-function( y,lambda)
{x <- -lambda*log(1-y)}
x=Cdf_Invs(y,lambda)
ks.test(x, "pexp",1/lambda)##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: x
## D = 0.045446, p-value = 0.03215
## alternative hypothesis: two-sidedhist(x,prob=TRUE,col = "blue",main="Distribucion Expoencial")
curve(dexp(x,1/lambda),xlab = "x",col="red",lwd=2, main="distribucion betha", add=TRUE)
rm(list=ls())
y<-runif(10,0,1)
Cdf_Invs<-function( y,a,b)
{(-b^a*log(1-y))^1/a}
a<-5
b<-12
x<-Cdf_Invs(y,a,b)
x## [1] 16713.2766 62438.6909 45754.1391 46717.9895 11671.5348 4030.9498
## [7] 149.1061 29702.1707 2662.4637 25101.0119ks.test(y,pweibull(a,b))##
## Exact two-sample Kolmogorov-Smirnov test
##
## data: y and pweibull(a, b)
## D = 1, p-value = 0.1818
## alternative hypothesis: two-sidedhist(x,prob=TRUE,col = "blue",main="Distribucion Pweibull")
curve(dweibull(x,a,b),xlab = "x",col="red", add=TRUE)
rm(list=ls())
y<-runif(100,0,1)
p<-0.25
Cdf_Invs<-function( y,p)
{ceiling(log(1-y)/log(1-p))-1}
x<-Cdf_Invs(y,p)
x## [1] 6 0 4 12 1 1 1 0 2 0 2 0 3 0 4 2 3 11 0 0 2 5 0 1 0
## [26] 0 4 14 2 6 3 0 3 0 5 1 6 9 3 10 8 1 1 0 2 6 1 0 1 0
## [51] 0 6 14 1 0 2 1 1 6 1 4 2 2 3 5 0 1 11 3 5 0 12 2 0 0
## [76] 1 0 0 1 1 1 0 11 0 0 9 0 0 0 4 1 2 6 1 3 3 9 2 7 6ks.test(x,pgeom,p)## Warning in ks.test.default(x, pgeom, p): ties should not be present for the
## Kolmogorov-Smirnov test##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: x
## D = 0.25, p-value = 7.453e-06
## alternative hypothesis: two-sidedhist(x,prob=TRUE,col = "blue",main="Distribucion Pgeometrica")
curve(dgeom(x,p),col="red",lwd=2, add=TRUE)## Warning in dgeom(x, p): non-integer x = 0.140000## Warning in dgeom(x, p): non-integer x = 0.280000## Warning in dgeom(x, p): non-integer x = 0.420000## Warning in dgeom(x, p): non-integer x = 0.560000## Warning in dgeom(x, p): non-integer x = 0.700000## Warning in dgeom(x, p): non-integer x = 0.840000## Warning in dgeom(x, p): non-integer x = 0.980000## Warning in dgeom(x, p): non-integer x = 1.120000## Warning in dgeom(x, p): non-integer x = 1.260000## Warning in dgeom(x, p): non-integer x = 1.400000## Warning in dgeom(x, p): non-integer x = 1.540000## Warning in dgeom(x, p): non-integer x = 1.680000## Warning in dgeom(x, p): non-integer x = 1.820000## Warning in dgeom(x, p): non-integer x = 1.960000## Warning in dgeom(x, p): non-integer x = 2.100000## Warning in dgeom(x, p): non-integer x = 2.240000## Warning in dgeom(x, p): non-integer x = 2.380000## Warning in dgeom(x, p): non-integer x = 2.520000## Warning in dgeom(x, p): non-integer x = 2.660000## Warning in dgeom(x, p): non-integer x = 2.800000## Warning in dgeom(x, p): non-integer x = 2.940000## Warning in dgeom(x, p): non-integer x = 3.080000## Warning in dgeom(x, p): non-integer x = 3.220000## Warning in dgeom(x, p): non-integer x = 3.360000## Warning in dgeom(x, p): non-integer x = 3.500000## Warning in dgeom(x, p): non-integer x = 3.640000## Warning in dgeom(x, p): non-integer x = 3.780000## Warning in dgeom(x, p): non-integer x = 3.920000## Warning in dgeom(x, p): non-integer x = 4.060000## Warning in dgeom(x, p): non-integer x = 4.200000## Warning in dgeom(x, p): non-integer x = 4.340000## Warning in dgeom(x, p): non-integer x = 4.480000## Warning in dgeom(x, p): non-integer x = 4.620000## Warning in dgeom(x, p): non-integer x = 4.760000## Warning in dgeom(x, p): non-integer x = 4.900000## Warning in dgeom(x, p): non-integer x = 5.040000## Warning in dgeom(x, p): non-integer x = 5.180000## Warning in dgeom(x, p): non-integer x = 5.320000## Warning in dgeom(x, p): non-integer x = 5.460000## Warning in dgeom(x, p): non-integer x = 5.600000## Warning in dgeom(x, p): non-integer x = 5.740000## Warning in dgeom(x, p): non-integer x = 5.880000## Warning in dgeom(x, p): non-integer x = 6.020000## Warning in dgeom(x, p): non-integer x = 6.160000## Warning in dgeom(x, p): non-integer x = 6.300000## Warning in dgeom(x, p): non-integer x = 6.440000## Warning in dgeom(x, p): non-integer x = 6.580000## Warning in dgeom(x, p): non-integer x = 6.720000## Warning in dgeom(x, p): non-integer x = 6.860000## Warning in dgeom(x, p): non-integer x = 7.140000## Warning in dgeom(x, p): non-integer x = 7.280000## Warning in dgeom(x, p): non-integer x = 7.420000## Warning in dgeom(x, p): non-integer x = 7.560000## Warning in dgeom(x, p): non-integer x = 7.700000## Warning in dgeom(x, p): non-integer x = 7.840000## Warning in dgeom(x, p): non-integer x = 7.980000## Warning in dgeom(x, p): non-integer x = 8.120000## Warning in dgeom(x, p): non-integer x = 8.260000## Warning in dgeom(x, p): non-integer x = 8.400000## Warning in dgeom(x, p): non-integer x = 8.540000## Warning in dgeom(x, p): non-integer x = 8.680000## Warning in dgeom(x, p): non-integer x = 8.820000## Warning in dgeom(x, p): non-integer x = 8.960000## Warning in dgeom(x, p): non-integer x = 9.100000## Warning in dgeom(x, p): non-integer x = 9.240000## Warning in dgeom(x, p): non-integer x = 9.380000## Warning in dgeom(x, p): non-integer x = 9.520000## Warning in dgeom(x, p): non-integer x = 9.660000## Warning in dgeom(x, p): non-integer x = 9.800000## Warning in dgeom(x, p): non-integer x = 9.940000## Warning in dgeom(x, p): non-integer x = 10.080000## Warning in dgeom(x, p): non-integer x = 10.220000## Warning in dgeom(x, p): non-integer x = 10.360000## Warning in dgeom(x, p): non-integer x = 10.500000## Warning in dgeom(x, p): non-integer x = 10.640000## Warning in dgeom(x, p): non-integer x = 10.780000## Warning in dgeom(x, p): non-integer x = 10.920000## Warning in dgeom(x, p): non-integer x = 11.060000## Warning in dgeom(x, p): non-integer x = 11.200000## Warning in dgeom(x, p): non-integer x = 11.340000## Warning in dgeom(x, p): non-integer x = 11.480000## Warning in dgeom(x, p): non-integer x = 11.620000## Warning in dgeom(x, p): non-integer x = 11.760000## Warning in dgeom(x, p): non-integer x = 11.900000## Warning in dgeom(x, p): non-integer x = 12.040000## Warning in dgeom(x, p): non-integer x = 12.180000## Warning in dgeom(x, p): non-integer x = 12.320000## Warning in dgeom(x, p): non-integer x = 12.460000## Warning in dgeom(x, p): non-integer x = 12.600000## Warning in dgeom(x, p): non-integer x = 12.740000## Warning in dgeom(x, p): non-integer x = 12.880000## Warning in dgeom(x, p): non-integer x = 13.020000## Warning in dgeom(x, p): non-integer x = 13.160000## Warning in dgeom(x, p): non-integer x = 13.300000## Warning in dgeom(x, p): non-integer x = 13.440000## Warning in dgeom(x, p): non-integer x = 13.580000## Warning in dgeom(x, p): non-integer x = 13.720000## Warning in dgeom(x, p): non-integer x = 13.860000
n<-1000
p<-0.3
set.seed(100)
u<-runif(n)
x<-as.integer(u>0.7)
x## [1] 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0
## [38] 0 1 0 0 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1
## [75] 0 0 1 1 1 0 0 0 1 1 0 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1
## [112] 1 0 0 1 0 1 1 0 1 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0
## [149] 0 0 0 1 0 0 0 1 1 1 0 0 1 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 0 0 1 1 0 0
## [186] 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0
## [223] 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0 1 1 0 0 0
## [260] 1 0 1 0 1 1 1 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0
## [297] 0 1 0 0 1 0 1 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 0 0
## [334] 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 1
## [371] 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0
## [408] 1 1 0 0 0 0 1 0 1 0 1 0 1 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 0
## [445] 0 1 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0
## [482] 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0
## [519] 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1 0 1 0 1 0
## [556] 1 1 0 0 0 1 0 0 1 1 0 1 0 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 1 0 0
## [593] 0 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0
## [630] 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 1 0 1 1 0 0 0 0 1 1 0 0
## [667] 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0 1 1 0 0 0 1 1 0 0 1 0 0 1
## [704] 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 1 1
## [741] 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0 0 1 0 1 1
## [778] 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1
## [815] 0 0 1 0 1 0 1 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1
## [852] 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 1 0 0 1 0 0 1
## [889] 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0
## [926] 0 0 1 0 1 0 1 0 0 1 1 0 1 0 1 1 1 0 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 0 1 0 0
## [963] 1 0 0 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 1 0 0 0
## [1000] 1mean(x)## [1] 0.321var(x)## [1] 0.2181772n<-10
p<-0.3
set.seed(10)
u<-runif(n)
x<-as.integer(u>1-p)
x## [1] 0 0 0 0 0 0 0 0 0 0mean(x)## [1] 0var(x)## [1] 0#geometrica
ceiling(5)## [1] 5ceiling(4.8)## [1] 5n<-1000
p<-0.25
set.seed(100)
u<-runif(n)
x<-ceiling(log(1-y)/log(1-p))-1
mean(x)## [1] 2.96var(x)## [1] 12.52364hist(x,prob=T,col="green",main="histograma de Geometrica")
n<-500 #n=500 datos
p<-0.30
mat<-matrix(0,
nrow = 1000,
ncol=500
)#
View(data.frame(mat))
dim(mat)## [1] 1000 500length(mat)## [1] 500000for (i in 1:n)
{u<-runif(n)# u igual ala uniforme con n datos=500
x<-as.integer(u>1-p)#funcion binomial,#length
mat[,i]<-x
}
View(data.frame(mat))
s<-apply(mat,2,mean)#tabla DE la media por columna,nrow=1 es igual afilas, ncol=columna
s## [1] 0.310 0.310 0.268 0.296 0.276 0.286 0.298 0.294 0.296 0.282 0.280 0.318
## [13] 0.290 0.272 0.290 0.284 0.318 0.300 0.308 0.250 0.320 0.306 0.254 0.300
## [25] 0.244 0.298 0.284 0.302 0.312 0.274 0.300 0.314 0.282 0.324 0.308 0.296
## [37] 0.318 0.344 0.294 0.304 0.292 0.266 0.286 0.282 0.306 0.268 0.274 0.306
## [49] 0.300 0.304 0.292 0.310 0.302 0.308 0.312 0.328 0.266 0.292 0.276 0.310
## [61] 0.318 0.318 0.268 0.316 0.302 0.302 0.298 0.284 0.288 0.284 0.296 0.288
## [73] 0.306 0.316 0.292 0.320 0.300 0.306 0.296 0.268 0.290 0.278 0.314 0.334
## [85] 0.270 0.302 0.314 0.332 0.266 0.272 0.304 0.282 0.310 0.258 0.268 0.294
## [97] 0.242 0.312 0.310 0.326 0.294 0.286 0.290 0.304 0.354 0.302 0.296 0.318
## [109] 0.268 0.336 0.298 0.292 0.326 0.324 0.298 0.316 0.264 0.350 0.286 0.268
## [121] 0.298 0.326 0.292 0.296 0.284 0.304 0.300 0.282 0.302 0.276 0.312 0.290
## [133] 0.290 0.270 0.300 0.254 0.304 0.306 0.280 0.294 0.288 0.302 0.290 0.318
## [145] 0.282 0.292 0.270 0.318 0.296 0.316 0.266 0.314 0.324 0.290 0.300 0.304
## [157] 0.306 0.304 0.296 0.266 0.322 0.314 0.318 0.320 0.326 0.310 0.326 0.312
## [169] 0.282 0.286 0.306 0.338 0.308 0.302 0.316 0.330 0.314 0.262 0.306 0.302
## [181] 0.260 0.294 0.324 0.276 0.326 0.308 0.296 0.288 0.298 0.266 0.296 0.298
## [193] 0.352 0.270 0.284 0.334 0.312 0.298 0.324 0.288 0.282 0.308 0.300 0.260
## [205] 0.284 0.300 0.302 0.246 0.318 0.296 0.286 0.330 0.286 0.276 0.312 0.336
## [217] 0.322 0.272 0.290 0.324 0.284 0.322 0.294 0.348 0.318 0.340 0.270 0.296
## [229] 0.280 0.316 0.308 0.308 0.254 0.316 0.292 0.322 0.282 0.298 0.274 0.262
## [241] 0.278 0.264 0.274 0.262 0.302 0.302 0.334 0.304 0.274 0.276 0.282 0.294
## [253] 0.294 0.278 0.282 0.288 0.282 0.346 0.300 0.308 0.330 0.284 0.294 0.310
## [265] 0.318 0.316 0.262 0.288 0.322 0.322 0.324 0.294 0.278 0.316 0.326 0.296
## [277] 0.310 0.312 0.322 0.296 0.284 0.326 0.278 0.298 0.302 0.300 0.306 0.304
## [289] 0.296 0.308 0.308 0.298 0.332 0.300 0.284 0.294 0.290 0.304 0.302 0.316
## [301] 0.318 0.274 0.296 0.312 0.308 0.322 0.340 0.302 0.240 0.278 0.286 0.308
## [313] 0.284 0.288 0.288 0.318 0.306 0.272 0.276 0.316 0.328 0.310 0.332 0.312
## [325] 0.340 0.282 0.312 0.268 0.280 0.282 0.268 0.288 0.294 0.324 0.280 0.316
## [337] 0.282 0.322 0.374 0.300 0.310 0.350 0.328 0.288 0.334 0.326 0.308 0.296
## [349] 0.288 0.304 0.318 0.300 0.254 0.282 0.300 0.288 0.300 0.280 0.290 0.282
## [361] 0.330 0.294 0.298 0.294 0.298 0.298 0.320 0.330 0.302 0.332 0.286 0.292
## [373] 0.292 0.260 0.318 0.288 0.288 0.272 0.274 0.326 0.298 0.320 0.270 0.284
## [385] 0.340 0.292 0.300 0.296 0.286 0.278 0.256 0.322 0.328 0.308 0.360 0.292
## [397] 0.312 0.314 0.300 0.284 0.286 0.278 0.300 0.304 0.284 0.356 0.300 0.316
## [409] 0.288 0.278 0.316 0.298 0.320 0.264 0.306 0.314 0.322 0.280 0.316 0.298
## [421] 0.278 0.314 0.292 0.306 0.302 0.296 0.300 0.298 0.294 0.294 0.296 0.282
## [433] 0.306 0.298 0.284 0.278 0.326 0.296 0.278 0.282 0.292 0.288 0.326 0.300
## [445] 0.320 0.312 0.282 0.320 0.298 0.330 0.300 0.316 0.300 0.310 0.250 0.298
## [457] 0.296 0.318 0.272 0.304 0.280 0.298 0.288 0.296 0.262 0.300 0.300 0.328
## [469] 0.288 0.308 0.300 0.290 0.292 0.308 0.316 0.314 0.290 0.272 0.296 0.308
## [481] 0.302 0.310 0.274 0.286 0.320 0.292 0.320 0.294 0.290 0.348 0.270 0.294
## [493] 0.298 0.310 0.292 0.296 0.288 0.324 0.298 0.290View(s)
#B<-apply(mat,1,mean)
##B
#View(B)###############
library(spgs)
n<-1000
u<-runif(n)
p<-0.4
x<-as.integer(u>0.6)
a<- diid.test(x)
a##
## Composite test for a Bernoulli scheme
## Data: x
## statistic p.value adjusted.p df method
## 1 11.748007 0.92448 0.92448 20 Box-Ljung test
## 2 0.033169 0.22121 0.44242 NA Uniform(0,1) Kolmogorov-Smirnov test
## Multiple testing method use to adjust p-values: holm
## minimum adjusted p-value = 0.44242
## sample estimates:
## 0 1
## 0.601 0.399attributes(x)## NULLrm(list = ls())
n<-1000
m<-100
p<-0.4
fun_ber<-function(n,p)
{u<-runif(n)
x<-as.integer(u >1-p)
return(x)
}
var_binom<-matrix(0,n,m)
for(i in 1:m)
{
var_binom[,i]<-fun_ber(n,p)}
View(var_binom)rm(list = ls())
n<-10000
m<-100
p<-0.4
fun_ber<-function(n,p)
{u<-runif(n)
x<-as.integer(u >1-p)
return(x)
}
var_berno<-matrix(0,n,m)
for(i in 1:m)
{
var_berno[,i]<-fun_ber(n,p)}
View(var_berno)
var_binom<-apply(var_berno,1,sum)
class(var_berno)## [1] "matrix" "array"hist(var_binom,col = "red")
rm(list = ls())
n<-10000
m<-100
p<-0.4
fun_ber<-function(n,p)
{u<-runif(n)
x<-as.integer(u >1-p)
return(x)
}
fun_mean_binom<-function(n,m,p)
{var_berno<-matrix(0,n,m)
for(i in 1:m)
{
var_berno[,i]<-fun_ber(n,p)
}
var_binom<-apply(var_berno,1,sum)
bar_x<-mean(var_binom)
return(bar_x)
}
mn<-500
x_bar<-as.numeric()
for(i in 1:mn)
{x_bar[i]<-fun_mean_binom(n,m,p)
}
x_bar## [1] 40.0095 39.9602 39.9901 40.0573 39.9550 40.0532 40.0096 40.0571 39.9689
## [10] 39.9368 40.0290 40.0401 40.0416 40.0343 40.0426 39.9988 40.0079 39.9547
## [19] 40.0164 39.9483 39.9718 39.9292 39.9033 39.9623 39.9833 39.9252 40.0423
## [28] 39.9463 40.0218 39.8928 39.9508 40.0041 39.9666 40.0186 39.9439 39.9571
## [37] 40.0516 39.9749 40.0252 40.0425 40.0306 40.0111 39.9300 39.9921 39.9626
## [46] 39.8990 39.9640 40.0130 40.0557 39.9497 40.0449 39.9613 40.0388 40.0237
## [55] 39.9389 39.9818 39.9927 40.0075 39.9289 39.9701 40.1220 40.0332 39.9461
## [64] 40.0110 39.9670 39.9942 40.0998 39.9671 40.0851 40.0308 40.0052 39.9980
## [73] 40.0485 40.0086 39.9749 39.9980 39.9912 39.9790 40.0187 40.0247 40.0170
## [82] 39.9832 39.9723 40.0373 39.9935 40.0196 39.9920 40.0312 39.9603 40.0758
## [91] 40.0035 39.9672 39.9069 40.0417 39.9758 39.9593 39.9825 39.9838 40.0250
## [100] 39.9763 39.9693 40.0036 39.9428 39.9755 39.9904 39.9137 40.0543 40.0284
## [109] 39.9703 40.0360 40.0805 40.0014 40.0792 40.0883 40.0908 40.0389 39.9257
## [118] 39.9544 40.0686 40.0432 39.9940 39.9831 40.0197 40.0783 40.0203 39.9791
## [127] 39.9498 39.9608 40.0064 39.9692 40.0442 39.9624 40.0253 39.9166 40.0084
## [136] 39.9729 40.1067 39.9768 39.9375 39.9931 40.0588 40.0150 40.0509 40.0572
## [145] 40.0604 40.0253 40.0607 40.0966 39.9121 39.9232 40.0175 39.9300 40.0328
## [154] 40.0290 39.9800 39.9953 39.9401 39.9781 40.0375 40.0105 39.9852 39.9939
## [163] 40.0713 40.0071 40.0230 40.0697 39.9456 39.9788 40.0411 39.9678 39.9956
## [172] 40.0209 39.9176 39.9962 40.0068 40.0083 39.9807 40.0145 39.9513 39.9513
## [181] 39.9650 39.9398 39.9479 40.0066 40.0305 40.0689 40.0197 39.9628 40.0042
## [190] 40.0561 40.0277 40.0252 39.9942 40.0185 40.0195 39.9717 40.0180 40.0273
## [199] 40.0468 40.1521 40.0018 40.0177 39.9996 40.0687 39.9450 40.0616 40.0082
## [208] 40.0413 39.9101 39.9399 40.0235 40.0539 39.9355 39.9731 39.9232 40.0182
## [217] 40.0795 40.0035 40.0078 39.9956 39.9719 40.0011 39.9270 40.0751 40.0470
## [226] 40.0192 39.9869 39.9678 39.9553 40.0408 39.9636 39.9214 40.0562 39.9262
## [235] 39.9561 40.0324 40.0643 40.0018 39.9270 39.9281 40.0050 39.9750 39.9171
## [244] 39.9821 40.0150 40.0454 40.0421 39.9292 39.9629 39.9911 40.0666 39.9674
## [253] 39.9688 40.0532 39.9929 40.0118 39.9606 39.8854 39.9780 39.9272 39.9115
## [262] 39.9630 40.0065 40.0496 40.0835 40.1171 39.9385 39.9668 39.9976 40.0054
## [271] 39.9764 40.0995 39.9991 40.0419 39.9969 40.0244 40.0434 40.0592 39.9575
## [280] 39.9629 40.1047 40.0031 40.0008 39.9548 39.9639 40.0052 39.8927 39.9949
## [289] 40.0276 39.9591 39.9038 40.0589 39.9835 39.9986 40.0245 40.0580 40.0829
## [298] 39.9632 40.0387 40.0163 40.0001 39.9480 39.9915 40.0497 40.0142 39.9645
## [307] 39.9995 39.9808 39.9529 39.9271 39.9708 40.0545 39.9726 40.0048 40.0287
## [316] 39.9856 40.0220 39.9501 40.0243 40.0400 40.0243 39.9888 40.0022 39.9539
## [325] 40.0094 39.9647 39.9742 39.9378 39.9953 40.0057 39.9874 40.0385 40.0341
## [334] 40.0338 40.0624 40.0931 39.9721 40.0927 40.0740 39.9060 39.9771 39.9682
## [343] 40.0976 40.0572 39.9962 40.0641 40.0274 39.8924 39.9825 39.9409 39.9489
## [352] 39.9834 39.9385 39.9832 40.0255 39.9714 39.9395 40.0115 40.0039 39.9487
## [361] 40.0228 40.0061 40.0520 39.9154 39.9813 40.0369 40.0505 39.8841 40.0104
## [370] 39.9194 40.0114 40.1141 40.0357 40.0651 40.0030 40.0463 40.0862 40.0940
## [379] 39.9949 39.9888 40.0960 40.0475 39.9990 39.9205 40.0342 40.0849 39.9924
## [388] 39.9960 40.0332 40.0200 40.1493 39.9481 40.0067 39.9809 39.9649 40.0201
## [397] 39.9970 39.9104 39.9721 39.9593 40.1061 39.9798 39.9000 40.0375 39.9854
## [406] 40.1330 40.0675 40.0304 40.0490 39.9748 39.9603 39.9172 39.9339 39.8955
## [415] 40.1260 39.9919 39.9424 39.9958 39.9994 40.0321 40.0218 39.9746 39.9956
## [424] 39.9763 39.9311 40.0264 40.0990 39.9563 40.0232 40.0071 39.9514 40.1005
## [433] 39.9708 39.9816 40.1189 39.9765 39.9741 40.0205 39.9546 39.9930 40.0591
## [442] 40.0761 39.9725 39.9860 40.0450 39.9893 40.0263 39.9930 40.0451 39.9710
## [451] 40.0010 39.9588 39.9870 39.9720 39.9332 40.0531 40.0052 39.9431 39.9539
## [460] 40.0528 40.0275 40.1006 39.9433 39.9900 40.0394 39.9945 39.9085 40.1124
## [469] 39.9672 39.9953 40.0687 39.9483 39.9294 40.0790 40.0263 40.0110 40.0431
## [478] 39.9995 39.9480 40.0441 40.0345 40.0262 40.0269 39.9495 39.9801 40.0461
## [487] 39.9911 40.0311 39.9767 40.1282 39.9591 40.0126 40.0680 40.0109 40.0772
## [496] 40.0798 40.0833 40.0334 40.0801 39.9782length(x_bar)## [1] 500hist(x_bar, col="blue",main = "distribucion Bernoulli")
x_bar.m<-mean(x_bar)
x_bar.sd<-sd(x_bar)
z<-(x_bar-x_bar.m)/x_bar.sd
hist(z)
ks.test(z,pnorm,0,1)## Warning in ks.test.default(z, pnorm, 0, 1): ties should not be present for the
## Kolmogorov-Smirnov test##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: z
## D = 0.027206, p-value = 0.853
## alternative hypothesis: two-sidedEl juego de hipotesis , esta dado por \[ H_0:z\sim N(0,1) \]
\[ H_a:z\nsim N(0,1) \]
\[ z= \frac{\bar{x}-E(\bar{x})}{\sqrt{var(\bar{x})) }} \]