R/mycltb.R

In DevinMcAfee123/MATH4753MCAFEE:

#' Title
#' @title Binomial Sample Mean Distribution
#' @param n sample size
#' @param iter number of samples
#' @param p probability of success associated with binomial population
#'
#' @return histogram comparing the sample mean distribution with the theoretical normal distribution anticipated by the central limit theorem
#' @export
#'
#' @examples
#' \dontrun{mycltb(n=20,iter=10000,p=0.3)}
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)
}