#--------- central.limit ---------------
#
#The input parameters are:
#	n - size of each sample 
#	m - number of samples of size n to select
#	qq - TRUE means show the Q-Q plots
#	df1, df2 - the df of the F() distribution from which samples are drawn
#	xlow, xhigh - x-axis limits for plots

central.limit = function(n=15,m=1000,qq=FALSE,df1=6,df2=200,xlow=0,xhigh=2.5) {

	means = vector() # I hereby declare that "means" is a vector

	for (i in 1:m) {  # get m samples from a skewed distribution
		data= rf(n,df1,df2)  # the F() distribution is nice and skewed
		means[i] = mean(data)  # means is our array of means
	}
	if (qq) {  # call with TRUE and it makes the q-q plots
		x=qqnorm(means)$x
		qqline(means)
		caption = paste("n =",n,", Correlation = ",signif(cor(means,x),3))
		mtext(caption)
	} else {  # the default behavior
		title = paste("Sample size = ",n)	
		hist(means, xlim = c(xlow,xhigh),main=title,freq=F)
		plot(function(x)dnorm(x,mean=mean(means), sd=sd(means)),xlow,xhigh,add=T)
		plot(function(x)df(x,df1,df2),xlow,xhigh,add=T)
		caption = paste("Standard error = ",signif(sd(means),3))
		mtext(caption)
	}
}