R/mycltb.R

In cbain1/MATH4753BAIN:

#' A Function to Use the Central Limit Theorem to Approximate a Normal Distribution Using the Binomial Theorem
#'
#' @param n the sample size
#' @param iter the number of times you want to sample
#' @param p the p-value
#' @param ... extra settings you may wish to pass into internal functions
#'
#' @return a plot
#' @export
#'
#' @examples
mycltb=function(n,iter,p=0.5,...){

	## r-random sample from the Binomial
	y=rbinom(n*iter,size=n,prob=p)
	## Place these numbers into a matrix
	## The columns will correspond to the iteration and the rows will equal the sample size n
	data=matrix(y,nr=n,nc=iter,byrow=TRUE)
	## apply the function mean to the columns (2) of the matrix
	## these are placed in a vector w
	w=apply(data,2,mean)
	## We will make a histogram of the values in w
	## How high should we make y axis?
	## All the values used to make a histogram are placed in param (nothing is plotted yet)
	param=hist(w,plot=FALSE)
	## Since the histogram will be a density plot we will find the max density

	ymax=max(param$density)
	## To be on the safe side we will add 10% more to this
	ymax=1.1*ymax

	## Now we can make the histogram
	## freq=FALSE means take a density
	hist(w,freq=FALSE,  ylim=c(0,ymax),
		 main=paste("Histogram of sample mean","\n", "sample size= ",n,sep=""),
		 xlab="Sample mean",...)
	## add a density curve made from the sample distribution
	#lines(density(w),col="Blue",lwd=3) # add a density plot
	## Add a theoretical normal curve
	curve(dnorm(x,mean=n*p,sd=sqrt(p*(1-p))),add=TRUE,col="Red",lty=2,lwd=3)

}