#
#  Figure 3.1  Examples of beta densities
#
par(mfrow=c(3,3))
par(lab=c(2,2,0))
par(yaxt="n")
par(mar=c(3.8,3.8,3.8,3.8))
betafn <- function(x) (beta(a,b))^(-1)*x^(a-1)*(1-x)^(b-1)
a <- 0.5
b <- 0.5
curve(betafn,0,1,n=1000,ylim=c(0,2.2),ylab="",xlab="",
main="(a)                                 \n\n")
par(mex=0.9)
# See plotmath for use of expression
mtext(expression(0<beta<1),side=3)
mtext(expression(0<alpha<1),side=2)
par(mex=1)
b <- 1.0
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
par(mex=0.9)
mtext(expression(beta==1),side=3)
par(mex=1)
b <- 1.5
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
par(mex=0.9)
mtext(expression(1<beta<2),side=3)
par(mex=1)
a <- 1.0
b <- 0.5
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
par(mex=0.9)
mtext(expression(alpha==1),side=2)
par(mex=1)
b <- 1.0
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
b <- 1.5
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
a <- 1.5
b <- 0.5
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
par(mex=0.9)
mtext(expression(1<alpha<2),side=2)
par(mex=1)
b <- 1.0
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
b <- 1.5
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
par(mfrow=c(3,3))
par(lab=c(2,2,0))
par(yaxt="n")
par(mar=c(3.8,3.8,3.8,3.8))
a <- 2.0
b <- 0.5
curve(betafn,0,1,n=1000,ylim=c(0,2.2),ylab="",xlab="",
main="(b)                                 \n\n")
par(mex=0.9)
# mtext(expression(0<beta<1),side=3)
mtext(expression(alpha==2),side=2)
par(mex=1)
b <- 1.0
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
par(mex=0.9)
# mtext(expression(beta==1),side=3)
par(mex=1)
b <- 1.5
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
par(mex=0.9)
# mtext(expression(1<beta<2),side=3)
par(mex=1)
a <- 2.5
b <- 0.5
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
par(mex=0.9)
mtext(expression(2<alpha<3),side=2)
par(mex=1)
b <- 1.0
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
b <- 1.5
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
a <- 3.0
b <- 0.5
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
par(mex=0.9)
mtext(expression(alpha==3),side=2)
par(mex=1)
b <- 1.0
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
b <- 1.5
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
par(mfrow=c(3,3))
par(lab=c(2,2,0))
par(yaxt="n")
par(mar=c(3.8,3.8,3.8,3.8))
a <- 0.5
b <- 2.0
curve(betafn,0,1,n=1000,ylim=c(0,2.2),ylab="",xlab="",
main="(c)                                 \n\n")
par(mex=0.9)
mtext(expression(beta==2),side=3)
mtext(expression(0<alpha<1),side=2)
par(mex=1)
b <- 2.5
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
par(mex=0.9)
mtext(expression(2<beta<3),side=3)
par(mex=1)
b <- 3.0
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
par(mex=0.9)
mtext(expression(beta==3),side=3)
par(mex=1)
a <- 1.0
b <- 2.0
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
par(mex=0.9)
mtext(expression(alpha==1),side=2)
par(mex=1)
b <- 2.5
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
b <- 3.0
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
a <- 1.5
b <- 2.0
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
par(mex=0.9)
mtext(expression(1<alpha<2),side=2)
par(mex=1)
b <- 2.5
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
b <- 3.0
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
par(mfrow=c(3,3))
par(lab=c(2,2,0))
par(yaxt="n")
par(mar=c(3.8,3.8,3.8,3.8))
a <- 2.0
b <- 2.0
curve(betafn,0,1,n=1000,ylim=c(0,2.2),ylab="",xlab="",
main="(d)                                 \n\n")
par(mex=0.9)
# mtext(expression(beta==2),side=3)
mtext(expression(alpha==2),side=2)
par(mex=1)
b <- 2.5
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
par(mex=0.9)
# mtext(expression(2<beta<3),side=3)
par(mex=1)
b <- 3.0
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
par(mex=0.9)
# mtext(expression(beta==3),side=3)
par(mex=1)
a <- 2.5
b <- 2.0
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
par(mex=0.9)
mtext(expression(2<alpha<3),side=2)
par(mex=1)
b <- 2.5
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
b <- 3.0
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
a <- 3.0
b <- 2.0
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
par(mex=0.9)
mtext(expression(alpha==3),side=2)
par(mex=1)
b <- 2.5
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
b <- 3.0
curve(betafn,0,1,n=1000,ylim=c(0,2.2),xlab="",ylab="")
par(mfrow=c(1,1))
par(lab=c(5,5,7))
par(yaxt="s")
par(mar=c(5.1,4.1,4.1,2.1))