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## Author: Joshua M. Tebbs
## Date: 22 October 2014
## Update: 5 July 2017
## STAT 712 course notes: R Code
## Chapters 1-5 (CB)
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# CHAPTER 1 #
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# Example 1.19
# Pages 24-25
# Discrete CDF
x = c(0,1,2)
prob = c(0.25,0.50,0.25)
# Plot CDF
cdf = c(0,cumsum(prob))
cdf.plot = stepfun(x,cdf,f=0)
plot.stepfun(cdf.plot,xlab="x",ylab="F(x)",verticals=FALSE,do.points=TRUE,main="",pch=16,cex.lab=1.25)

# Example 1.20
# Pages 26-27
# Exponential CDF
y = seq(0,10,0.001)
# Plot CDF
cdf = pexp(y,0.5)
plot(y,cdf,type="l",xlab="x",ylab="F(x)",xlim=c(-1,10),ylim=c(0,1),cex.lab=1.25)
abline(h=0)
abline(v=0,lty=2)

# Example 1.21
# Pages 28-29
# Poisson PMF and CDF
y = seq(0,15,1)
prob = dpois(y,5)
# Plot PMF
plot(y,prob,type="h",xlab="x",ylab="f(x)",cex.lab=1.25)
abline(h=0)
# Plot CDF
cdf = c(0,cumsum(prob))
cdf.plot = stepfun(y,cdf,f=0)
plot.stepfun(cdf.plot,xlab="x",ylab="F(x)",verticals=FALSE,do.points=TRUE,main="",pch=16,cex.lab=1.25)

# Example 1.22
# Pages 30-31
# Continuous PDF and CDF
x = seq(-6,6,0.001)
pdf = 0.5*exp(-abs(x))
# Plot PDF
plot(x,pdf,type="l",xlab="x",ylab="f(x)",ylim=c(0,0.5),cex.lab=1.25)
abline(h=0)
# Plot CDF
x.1 = seq(-6,0,0.001)
x.2 = seq(0.001,6,0.001)
cdf = c(0.5*exp(x.1),1-0.5*exp(-x.2))
plot(x,cdf,type="l",xlab="x",ylab="F(x)",ylim=c(0,1),cex.lab=1.25)
abline(h=0)

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# CHAPTER 2 #
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# Example 2.2
# Pages 36-38
# Plot of g(x)=x(1-x)
x = seq(0,1,0.001)
g = x*(1-x)
plot(x,g,type="l",xlab="x",ylab="y = g(x)",ylim=c(0,0.25),cex.lab=1.25)
abline(h=0)
# Pdf of X
pdf = 1+x-x
plot(x,pdf,type="l",xlab="x",ylab="f(x)",ylim=c(0,1.5),cex.lab=1.25)
abline(h=0)
# Pdf of Y
y = seq(0.001,0.25,0.001)
pdf = 2*(1-4*y)^(-1/2)
plot(y,pdf,type="l",xlab="y",ylab="f(y)",ylim=c(0,25),cex.lab=1.25)
abline(h=0)
abline(v=1/4,lty=2)

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# CHAPTER 3 #
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# NONE

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# CHAPTER 4 #
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# Example 4.3
# Pages 86-88
# Support in Example 4.3
x <- seq(0,1,0.01)
y1 <- x
y2 <- x-x
plot(x,y1,type="l",bty="L",xlab="x",ylab="y",cex.lab=1.25)
points(x,y2,type="l",col="black")
polygon(c(x,rev(x)),c(y2,rev(y1)),col="grey")

# Example 4.5
# Pages 89-90
# Marginal PDF of X
x = seq(0,1,0.001)
pdf = 4*x^3
plot(x,pdf,type="l",xlab="x",ylab="f(x)",ylim=c(0,4),cex.lab=1.25)
abline(h=0)
abline(v=1,lty=2)
# Marginal PDF of Y
y = seq(0,1,0.001)
pdf = 4*y*(1-y^2)
# Plot PDF
plot(y,pdf,type="l",xlab="y",ylab="f(y)",ylim=c(0,1.6),cex.lab=1.25)
abline(h=0)

# Example 4.6
# Pages 90-92
# PDF of Z
z = seq(0,10,0.001)
pdf = 1/((1+z)^2)
plot(z,pdf,type="l",xlab="z",ylab="f(z)",ylim=c(0,1),cex=1.25)
abline(h=0)
abline(v=0,lty=2)

# Example 4.9
# Pages 96-97
# Conditional PDFs
y = seq(2,10,0.001)
pdf = exp(2-y)
# PDF of Y given X=x
plot(y,pdf,type="l",xlab="y",ylab="f(y|x=2)",xlim=c(0,10),ylim=c(0,1),cex=1.25)
abline(h=0)
abline(v=2,lty=2)
x = seq(0,5,0.001)
pdf = 0.2+x-x
# PDF of X given Y=y
plot(x,pdf,type="l",xlab="x",ylab="f(x|y=5)",xlim=c(0,5),ylim=c(0,0.3),cex=1.25)
abline(h=0)

#############
# CHAPTER 5 #
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# Example 5.4
# Pages 142-143
# Triangular distribution
y1 = seq(0,1,0.001)
y2 = seq(1.001,2,0.001)
pdf1 = y1
pdf2 = 2-y2
y = c(y1,y2)
pdf = c(pdf1,pdf2)
# Plot PDF
plot(y,pdf,type="l",xlab="z",ylab="f(z)",ylim=c(0,1),cex=1.25)
abline(h=0)

# Example 5.9
# Pages 158-159
# Exponential order statistics
x = seq(0,20,0.001)
n=10
b=2
pdf.min = dexp(x,n/b)
pdf.max = n*dexp(x,1/b)*(1-exp(-x/b))^(n-1)
# Plot PDF.min
plot(x,pdf.min,type="l",xlab="x",ylab="PDF of minimum",xlim = c(0,2),ylim=c(0,5),cex=1.25)
abline(h=0)
abline(v=0,lty=2)
# Plot PDF.max
plot(x,pdf.max,type="l",xlab="x",ylab="PDF of maximum",xlim = c(0,17.5),ylim=c(0,0.2),cex=1.25)
abline(h=0)

# Example 5.13
# Pages 163-164
# ECDF
Fn <- ecdf(rnorm(250)) # for sample size n=250
plot(Fn,verticals = FALSE,do.points = FALSE, xlab="",ylab="",main ="",axes=FALSE)
par(new=T)
a <- seq(-3.5,3.5,0.01)
b <- pnorm(a)
plot(a,b,type="l",xlab="x",ylab="F(x)",cex=1.25)