# Edps 590BAY
# Fall 2019
# C.J.Anderson
#
# Impact on Binomial of 
#        (a) var x mean
#        (b) n with fixed p
#        (c) p or theta with fixed n
#
# Impact on Beta of
#        (d) a=b
#        (e) right skewed  a<b
#        (f) left skewed   a>b
#

#
# Plot variance x mean of binomial distribution
#
par(mfrow=c(1,1))
p <- seq(from=0, to=1, length.out=1000)
mu <- 20*p
var <- 20*p*(1-p)
plot(mu,var,type='l',main="Binomial n=20: variance x mean",
     xlim=c(0,20),xlab="Mean",
     ylab="Variance")

#
# Some example of binomial distributions
#
par(mfrow=c(2,2))
# (b)
y10 <- seq(from=0, to=10)
y20 <- seq(from=0, to=20)
y50 <- seq(from=0, to=50)
y100 <- seq(from=0, to=100)

bin10 <- dbinom(y10,10,.5)
bin20 <- dbinom(y20,20,.5)
bin50 <- dbinom(y50,50,.5)
bin100 <- dbinom(y100,100,.5)

plot(y10,bin10, type='h', main="n=10, p=.5")
plot(y20,bin20, type='h',main="n=20, p=.5")
plot(y50,bin50, type='h', main="n=50, p=.5")
plot(y100,bin100, type='h',main="n=100, p=.5")

# (c) 

bin.1 <- dbinom(y20,20,.1)
bin.3 <- dbinom(y20,20,.3)
bin.7 <- dbinom(y20,20,.7)
bin.95 <- dbinom(y20,20,.95)

plot(y20,bin.1, type='h', main="n=20, p=.1")
plot(y20,bin.3, type='h',main="n=20, p=.3")
plot(y20,bin.7, type='h', main="n=20, p=.7")
plot(y20,bin.95, type='h',main="n=20, p=.95")

################################################
# For beta and less typing,  use function      #
################################################
beta.plot <- function(a,b){
    y <- seq(from=0, to=1, length.out=1000)
    beta.ab <- dbeta(y,a,b)
    plot(y,beta.ab,type='l',main=paste("Beta(",a,",",b,")"),lwd=2,
         ylab="Density", xlim=c(0,1))
}
#
# Examples of beta distribution
#
#(d)

par(mfrow=c(2,2))

beta.plot(0.1,0.1)
beta.plot(1,1)
beta.plot(2,2)
beta.plot(5,5)

# (e)

par(mfrow=c(2,2))

beta.plot(0.1,1)
beta.plot(1,2)
beta.plot(2,3)
beta.plot(3,4)

# (f)

par(mfrow=c(2,2))

beta.plot(1,0.1)
beta.plot(2,1)
beta.plot(3,2)
beta.plot(4,3)

# (g)  --- not in lecture notes

par(mfrow=c(2,2))

beta.plot(.1,.1)
beta.plot(.8,.8)
beta.plot(.7,3)
beta.plot(3,.7)