triplet of Beta, Binomial, and Negative Binomial distribution

binom_beta_nbinom.R

library(ggplot2)

NB_p <- function(p,x,r){
  pnbinom(x, size = r, prob = p,lower.tail = TRUE)  
}

B_p <- function(p,x,r){
  pbinom(r-1, size = r+x, prob = p, lower.tail = FALSE)  
}

Beta_p <- function(p,x,r){
  pbeta(p, shape1 = r, shape2 = x+1, lower.tail = TRUE)
}

params = list(r = 10, x = 6)

pp = ggplot()+
  stat_function(fun = B_p, args = params, aes(linetype="binomial", colour="binomial"))+
  stat_function(fun = Beta_p, args = params, aes(linetype="beta", colour="beta"))+
  stat_function(fun = NB_p, args = params, aes(linetype="negative binomial", colour="negative binomial"))+
  stat_function(geom = "point", fun = B_p, args = params, aes(shape="binomial", colour="binomial"), n=7)+
  stat_function(geom = "point", fun = Beta_p, args = params, aes(shape="beta", colour="beta"), n=8)+
  stat_function(geom = "point", fun = NB_p, args = params, aes(shape="negative binomial", colour="negative binomial"), n=9)+
  xlim(c(0.001,0.999))+
  labs(x="p", y="probability",  colour="function", linetype="function",shape="function")+
  theme_bw()

print(pp)
ggsave(filename = "betacdf3.png", plot = pp, width = 7, height = 7)