test.Rmd

---
title: "Test Notebook"
output: html_notebook
---

### Implement the pseudo-random number generator: Xi = 16807Xi-1 mod (231-1). Using the seed X0 = 1234567, run the generator for 100,000 observations. Perform a chi-square goodness-of-fit test on the resulting PRN’s. Use 20 equal-probability intervals and level α = 0.05. Now perform a runs up-anddown test with α = 0.05 on the observations to see if they are independent.


```{r}
X<-c(1234567)
a<-16807
c<-1
m<-(2^31)-1
n<-10000
for (i in 1:n){
X[i+1] <- (a*X[i]+c)%%m
}

R<-X/m

##To perform Chi-Square Test
chisq.test(R)

##Creating a interval
intervals <- seq(0,1,by=0.05)
O <- rep(0,20)
for (i in 1:length(R)){
for (j in 1:20){
if(intervals[j] < R[i] && R[i] <= intervals[j+1]){
O[j] <- O[j] + 1
}
}
}
O
library(lawstat)
runs.test(R)
```


```{r}

normrandbm <- function(){
  U1 <- runif(1,0,1)
  U2 <- runif(1,0,1)
  X <- ((-2*log(U1))^(0.5))*cos(2*pi*U2)
  Y <- ((-2*log(U1))^(0.5))*sin(2*pi*U2)
  variables <- c("X" = X,"Y" = Y)
  return(variables)
}

normrandbm()
df <- data.frame("X", "Y")
bmstats <- function(n){
  
  for(i in 1:n){
    newData <- normrandbm()
    names(newData) <- c("X", "Y")
    rbind(df, newData)
  }
  return()
}

bmstats(5)
df
```