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## Author: Joshua M. Tebbs
## Date: 11 December 2011
## Update: 29 December 2017
## STAT 509 course notes: R Code
## Chapter 3
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# Example 3.1
# Page 19-22
# Discrete PMF and CDF
y = c(0,1,2,3,4,5,6)
prob = c(0.10,0.15,0.20,0.25,0.20,0.06,0.04)
# Plot PMF
plot(y,prob,type="h",xlab="y",ylab="PMF",ylim=c(0,max(prob)),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="y",ylab="CDF",verticals=FALSE,do.points=TRUE,main="",pch=16,cex.lab=1.25)


# Example 3.2
# Page 22-24
# Discrete PMF and CDF
y = c(0,1,2,3)
prob = c(0.20,0.30,0.30,0.20)
# Plot PMF
plot(y,prob,type="h",xlab="y",ylab="PMF",ylim=c(0,max(prob)),xaxp=c(0, 3, 3),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="y",ylab="CDF",verticals=FALSE,do.points=TRUE,main="",pch=16,cex.lab=1.25)


# Example 3.3
# Page 26-27
# Binomial PMF and CDF
y = c(0,1,2,3,4)
prob = dbinom(y,4,0.4)
# Plot PMF
plot(y,prob,type="h",xlab="y",ylab="PMF",ylim=c(0,max(prob)),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="y",ylab="CDF",verticals=FALSE,do.points=TRUE,main="",pch=16,cex.lab=1.25)


# Example 3.4
# Page 27-29
# Binomial PMF and CDF
y = seq(0,30,1)
prob = dbinom(y,30,0.1)
# Plot PMF
plot(y,prob,type="h",xlab="y",ylab="PMF",ylim=c(0,max(prob)),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="y",ylab="CDF",verticals=FALSE,do.points=TRUE,main="",pch=16,cex.lab=1.25)


# Example 3.5
# Page 30-31
# Geometric PMF and CDF
y = seq(1,25,1)
prob = dgeom(y-1,0.25)
# Plot PMF
plot(y,prob,type="h",xlab="y",ylab="PMF",ylim=c(0,max(prob)),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="y",ylab="CDF",verticals=FALSE,do.points=TRUE,main="",pch=16,cex.lab=1.25)


# Example 3.6
# Page 32-34
# Negative binomial PMF and CDF
y = seq(3,70,1)
prob = dnbinom(y-3,3,0.15)
# Plot PMF
plot(y,prob,type="h",xlab="y",ylab="PMF",ylim=c(0,max(prob)),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="y",ylab="CDF",verticals=FALSE,do.points=TRUE,main="",pch=16,cex.lab=1.25)


# Example 3.7
# Page 35-36
# Hypergeometric PMF and CDF
y = seq(0,5,1)
prob = dhyper(y,10,100-10,5)
# Plot PMF
plot(y,prob,type="h",xlab="y",ylab="PMF",ylim=c(0,max(prob)),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="y",ylab="CDF",verticals=FALSE,do.points=TRUE,main="",pch=16,cex.lab=1.25)


# Example 3.8
# Page 37-38
# Poisson PMF and CDF
y = seq(0,10,1)
prob = dpois(y,2.5)
# Plot PMF
plot(y,prob,type="h",xlab="y",ylab="PMF",ylim=c(0,max(prob)),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="y",ylab="CDF",verticals=FALSE,do.points=TRUE,main="",pch=16,cex.lab=1.25)