#' @title mycltu
#' @description Plots a random uniform distribution to show how the distribution changes with sample size.
#'
#' @param n number of different observations.
#' @param iter number of iterations.
#' @param a minimum values
#' @param b maximum value
#'
#' @importFrom graphics hist
#' @importFrom stats runif
#' @importFrom stats dunif
#' @importFrom graphics lines
#' @importFrom stats density
#' @export
mycltu <- function(n,iter,a=0,b=10){
# Random uniform theorem
y=runif(n*iter,a,b)
# Makes a matrix of the data from y
data=matrix(y,nrow=n,ncol=iter,byrow=TRUE)
# Calculates mean of the column
w=apply(data,2,mean)
# stores a histogram of w into param
param=hist(w,plot=FALSE)
# sets yman to 1.1x the max value in the density data
ymax=max(param$density)
ymax=1.1*ymax
# makes histogram
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=(a+b)/2,sd=(b-a)/(sqrt(12*n))),add=TRUE,col="Red",lty=2,lwd=3) # add a theoretical curve
# Add the density from which the samples were taken
curve(dunif(x,a,b),add=TRUE,lwd=4)
}
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