1. Display the beta-binomial distribution cdf in png format for various values of alpha and beta and fixed n

require(VGAM)

create.beta.binomial.cdf <- function(N, alpha_v,beta_v,colour="black", pch=16) {

n <- max(length(N),length(alpha_v),length(colour),length(pch))
N <- rep(N,length=n); alpha_v <- rep(alpha_v,length=n)
colour <- rep(colour,length=n); pch <- rep(pch,length=n);labels=NULL 

add.one.series <- function(N, alpha_v,beta_v, colour, pch, maxN) {
  cdf <- pbetabin.ab(0:N, N, alpha_v,beta_v,log=FALSE)

  for (i in 1:N) lines (c(i-1,i), c(cdf[i], cdf[i]), type="s", col=colour)
  lines(c(N,maxN), c(1, 1), type="s", col=colour)
  points(0:N, cdf, col=colour, pch=pch)
}
par(lwd=1, cex=1, mar=c(5,4,2,2)+.1)
plot(x= c(0,max(N)),y=c(0,1),xlab=expression(italic(k)),
 ylab=expression(P(italic(X >= k))),type="n" ,main="")

 axis(1, at=0:(max(N)), lab=0:(max(N)),font.lab=5)
 
for (i in 1:n)
  add.one.series(N[i],alpha_v[i],beta_v[i],col=i,pch[i], max(N))
  

for(i in 1:n){ labels=c(labels,as.expression(bquote(paste(alpha==.(alpha_v[i]),", ", beta==.(beta_v[i])))))

}

legend("bottomright", inset=.05, title=paste("n=",max(N)),legend=labels

, pch=19,lty=1, col=1:n,bty="n") }

png("beta-binomial cdf.png") create.beta.binomial.cdf(10,c(.2,.7,2,600),c(.25,2,2,400)) dev.off()

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