brr (version 1.0.0)

BNBDist: Beta-negative binomial distribution

Description

Density, cumulative function, quantile function and random generation for the Beta-negative binomial distribution with shape parameters a, c, d.

Usage

dbeta_nbinom(x, a, c, d, ...)
pbeta_nbinom(q, a, c, d, ...)
qbeta_nbinom(p, a, c, d, ...)
rbeta_nbinom(n, a, c, d)
sbeta_nbinom(a, c, d)
summary_beta_nbinom(a, c, d, output = "list", ...)

Arguments

x,q

vector of non-negative integer quantities

a,c,d

non-negative shape parameters

...

other arguments passed to ghyper

p

vector of probabilities

n

number of observations to be sampled

output

type of the summary_beta_nbinom output: "list" to return a list, "pandoc" to print a table

Value

dbeta_nbinom gives the density, pbeta_nbinom the cumulative function, qbeta_nbinom the quantile function, rbeta_nbinom samples from the distribution, sbeta_nbinom and summary_beta_nbinom give some summaries of the distribution.

Details

This is the mixture distribution obtained by sampling a value $b$ from a Beta distribution with parameters $c$, $d$, then sampling a value $\lambda$ from a Gamma distribution with shape $a$ and rate $b/(1-b)$, and then sampling a Poisson distribution with mean $\lambda$.

Examples

a <- 2 ; c <- 5 ; d <- 30
barplot(dbeta_nbinom(0:50, a, c, d), names=0:50)
summary_beta_nbinom(a, c, d)