######################
#MATH 4311 R Examples#
#QQ PLots            #
######################



#############
#EXPONENTIAL#
#############


#Generating Exponential Data
X=rexp(1000,rate=1/20)    #Rate = lambda = 1/theta

#Verifying the correct mean and distribution
mean(X)
hist(X,breaks=50)

#Sample Quantiles for Exponential Data
X=sort(X)
sample.quantiles.exp=X

#Theoretical Quantiles for Exponential Distribution
r=1:1000
p=r/(1000+1)
theoretical.quantiles.exp=qexp(p)

#QQ-plot comparing EXP to EXP (plot is linear, since sample matches population)
plot(sample.quantiles.exp,theoretical.quantiles.exp)


#############
#NORMAL DATA#
#############


#Generating Normal Data
X=rnorm(1000,mean=100,sd=15)    

#Verifying the correct mean, sd, and distribution
mean(X)
sd(X)
hist(X,breaks=50)

#Sample Quantiles for Normal Data
X=sort(X)
sample.quantiles.norm=X

#Theoretical Quantiles for Normal Distribution
r=1:1000
p=r/(1000+1)
theoretical.quantiles.norm=qnorm(p)

#QQ-plot comparing NORM to NORM (plot is linear, since sample matches population)
plot(sample.quantiles.norm,theoretical.quantiles.norm)



#############
#COMPARISONS#
#############

#Exponential sample to exponential distribution (linear/matching)
plot(sample.quantiles.exp,theoretical.quantiles.exp)


#Normal sample to normal distribution (linear/matching)
plot(sample.quantiles.norm,theoretical.quantiles.norm)


#Exponential sample to normal distribution (curved/not matching)
plot(sample.quantiles.exp,theoretical.quantiles.norm)


#Normal sample to exponential distribution (curved/not matching)
plot(sample.quantiles.norm,theoretical.quantiles.exp)