Beta-negative binomial distribution

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Description

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

Usage

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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

Details

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

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.

Note

BNBDist is a generic name for the functions documented.

Examples

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

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