# ISC4244c - Hypothesis testing
# Dennis E. Slice (c) 2012

# Clean house
rm(list=ls())

# q-q plots
# Define a function for repeated use of same code.
plot.cdf <- function(nSamples=0, nObs=100) {
# For several samples
# Set up the plot
x = seq(-4,4,0.1)
y = dnorm(x)
title = "N(0,1) cdf"
subtitle=""
if (nSamples) subtitle = paste("nSamples=",nSamples," nObservation=",nObs,sep="") 
# The pdf with dotted lines
plot(x,y,main=title,sub=subtitle, type="l",lwd=3,lty=3,ylim=c(0,1))
# Now, the cdf with thick line.
lines(x,cumsum(y/sum(y)),lwd=3,col="red")
# Now, as many empirical cdfs as requested. Default = 0.
if (nSamples) {
	for (i in 1:nSamples) {
		# Compute the cumulative values for a sample of n
		y1 = rep(1/nObs,nObs)
		y1 = cumsum(y1)
		# Now some sorted, matching random values.
		x1 = sort(rnorm(nObs))
		lines(x1,y1,lwd=1)
	}
}
}

par(ask=TRUE)
# N(0,1) pdf
x = seq(-4,4,0.1)
y = dnorm(x)
plot(x,y,main="N(0,1) pdf",type="l",lwd=3,ylim=c(0,1))

plot.cdf()
cat("Use 'plot.cdf(nSamples=0, nObs=100)' to plot empirical cdfs.")