###############
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  20.40211 0.43304    0.86608 20 Box-Ljung test                      
## 2   0.01914 0.85725    0.86608 NA Uniform(0,1) Kolmogorov-Smirnov test
## Multiple testing method use to adjust p-values:   holm 
## minimum adjusted p-value = 0.86608 
## sample estimates:
##     0     1 
## 0.603 0.397
attributes(x)
## NULL
rm(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] 39.9900 40.0697 39.9983 39.9211 40.0185 40.0230 40.1595 40.0319 39.9158
##  [10] 40.0168 39.9662 39.9604 40.0215 39.9834 40.0402 40.0545 39.9655 39.9611
##  [19] 39.9962 40.0596 40.0411 40.1072 40.0345 40.0376 40.0154 39.9515 40.0211
##  [28] 39.9810 39.9999 39.9738 40.0408 39.9695 40.0598 39.8314 40.0129 40.0568
##  [37] 40.0247 39.9860 40.0582 40.0056 40.0701 39.9601 40.0979 39.9415 40.0098
##  [46] 39.9932 40.0028 40.0068 39.9979 39.9965 40.0082 39.9892 39.9783 40.0672
##  [55] 40.0129 40.0312 40.0604 39.9707 40.0102 39.9451 39.9914 40.0325 39.9577
##  [64] 39.9881 39.9586 40.0203 40.0164 40.0093 39.9461 40.0444 40.0151 39.9621
##  [73] 40.0434 39.9440 40.0567 40.0941 40.1398 39.9808 39.9745 40.0100 40.0946
##  [82] 40.1173 40.0165 40.0123 40.0696 39.9663 39.9425 40.0173 40.0695 40.0195
##  [91] 40.0635 39.9431 39.9996 39.9651 40.0259 39.9593 39.9374 40.0362 39.9651
## [100] 40.0501 40.0458 40.0191 39.9225 39.9710 39.9302 40.0586 39.9457 40.0473
## [109] 39.9936 40.0299 39.9646 40.0137 39.9798 40.0354 40.1018 40.0018 40.0026
## [118] 39.8693 39.9382 39.9933 40.0626 40.0775 40.1306 39.9470 39.9695 39.9986
## [127] 40.0154 40.0119 39.9636 40.0102 39.9132 40.0199 40.0625 40.0109 39.9915
## [136] 39.9711 39.9941 39.9892 39.9967 39.9661 40.0555 39.9465 40.0177 39.9547
## [145] 39.9798 40.0492 40.0619 39.9719 40.0253 40.0684 39.9227 39.9991 40.0313
## [154] 39.9184 39.8854 39.9666 40.0436 40.0411 39.9089 40.0399 39.9997 39.9938
## [163] 39.9654 39.9617 40.0096 40.0509 40.0958 40.1063 40.0049 40.0936 39.9210
## [172] 39.9302 40.0292 39.9288 40.0210 39.9638 39.9785 39.9865 39.9834 40.0403
## [181] 39.9956 39.9454 40.0287 40.0219 39.9820 40.0353 40.0004 39.9534 39.9119
## [190] 39.9222 40.0128 39.9239 40.0169 40.0931 39.9783 39.9977 39.9255 39.9345
## [199] 40.0131 40.0250 40.0432 40.0694 39.9661 40.0208 39.9883 39.9597 40.0849
## [208] 40.0212 40.0526 40.0172 40.0210 40.0733 39.9618 40.0404 39.9710 40.0088
## [217] 40.0527 40.0399 39.9388 40.0054 39.9992 40.0439 40.0529 40.0138 39.9878
## [226] 40.0457 40.0253 39.9444 40.0044 40.0216 40.0779 39.9727 40.0430 39.9685
## [235] 40.0722 39.9552 39.9906 40.0396 40.0310 40.0121 39.9283 40.0205 40.0517
## [244] 40.0598 40.0262 40.0477 39.9678 39.9908 39.9384 40.0511 40.0563 39.9801
## [253] 40.0141 39.9309 40.0458 40.0228 40.0127 39.9961 40.0082 40.0525 39.9627
## [262] 39.9378 40.0251 39.9418 40.0466 39.9576 40.0470 39.9905 39.9949 39.9839
## [271] 40.0027 40.0291 39.8587 40.0361 39.9759 39.8742 39.9732 39.9424 39.9742
## [280] 40.0081 40.0145 39.9594 39.9875 39.9906 39.9376 39.9577 40.0402 40.0322
## [289] 39.9859 39.9805 39.8821 40.0171 40.0145 40.0395 39.9736 39.9532 39.9968
## [298] 39.9437 39.9530 39.9438 40.0523 39.9212 40.0034 40.0189 39.9566 40.0268
## [307] 40.0009 39.9702 39.9818 40.0562 39.9707 39.9624 40.0129 40.0162 39.9959
## [316] 40.0759 40.0337 40.0272 39.9069 39.9779 40.0347 40.0801 39.9759 40.0746
## [325] 39.9708 40.0130 39.9502 40.0096 40.0231 40.0276 39.9807 39.9568 40.0212
## [334] 39.9726 39.9251 40.1047 40.0081 40.0177 40.0157 39.9764 40.0422 39.9747
## [343] 40.0352 40.0599 40.0050 40.0255 39.9728 40.0186 39.9785 39.9996 40.0281
## [352] 39.9831 40.0527 39.9165 39.9274 40.0237 40.0490 40.0301 39.9510 39.9694
## [361] 40.1371 40.0584 39.9511 40.0002 40.0172 40.0086 39.9881 39.9698 40.0439
## [370] 40.0280 39.9859 40.0341 39.9637 40.0522 40.0048 39.9772 40.0031 39.9625
## [379] 40.0176 40.0933 40.0235 40.0043 40.0149 39.9850 39.9448 40.0119 39.9141
## [388] 39.9927 40.0143 39.9969 40.0900 39.9894 40.0743 40.0210 40.0245 39.9533
## [397] 40.0517 40.0204 39.9459 40.0970 39.9529 40.1087 40.0228 39.9167 40.0211
## [406] 39.9807 40.0254 40.0730 39.9873 40.0623 39.9510 39.9392 40.0297 40.0461
## [415] 39.9391 40.0596 39.9133 39.9781 39.9601 40.0453 40.0567 39.9509 39.9927
## [424] 40.0969 40.0296 40.0273 39.9948 39.9178 40.0306 39.9036 40.0003 40.0620
## [433] 39.9713 39.9678 40.0465 40.0483 40.0537 39.8971 40.0673 40.0052 39.9317
## [442] 39.9195 40.0381 40.0129 39.9546 40.0131 40.0383 40.0372 40.0268 40.0194
## [451] 39.9458 39.9687 39.9406 40.0174 40.0377 40.0206 40.0460 40.0042 40.0021
## [460] 40.0636 39.9840 40.0738 39.9843 39.9783 40.0707 39.9766 39.9418 40.0751
## [469] 40.0020 39.9399 39.9795 40.0267 39.9925 39.9896 39.9938 40.0076 40.0849
## [478] 40.0430 40.0307 39.9821 39.9545 39.9909 39.9467 40.0110 40.0185 40.0751
## [487] 40.0203 39.9609 40.0359 40.0203 39.9710 39.9983 39.9235 40.0052 40.0543
## [496] 39.9279 39.9865 39.9729 39.9684 39.9717
length(x_bar)
## [1] 500
hist(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 = 0.035431, p-value = 0.5568
## alternative hypothesis: two-sided

El juego de hipotesis , esta dado por \[ H_0:z\sim N(0,1) \]

\[ H_a:z\nsim N(0,1) \]

\[ z= \frac{\bar{x}-E(\bar{x})}{\sqrt{var(\bar{x})) }} \]