The Beta-binomial Distribution

Cumulative density & mass functions, and random number generation for the Beta-binomial distribution using the following re-parameterisation of the Stan Beta-binomial definition:

• mu = alpha * beta mean probability of trial success.

• phi = (1 - mu) * beta precision or over-dispersion, component.

Usage

dbeta_binomial(x, size, mu, phi, log = FALSE)

pbeta_binomial(q, size, mu, phi, lower.tail = TRUE, log.p = FALSE)

qbeta_binomial(p, size, mu, phi, lower.tail = TRUE, log.p = FALSE)

rbeta_binomial(n, size, mu, phi)

Arguments

x, q

Vector of quantiles.

size

Vector of number of trials (zero or more).

mu

Vector of means.

phi

Vector of precisions.

log

Logical; If TRUE, values are returned on the log scale.

lower.tail

Logical; If TRUE (default), return P(X <= x). Else, return P(X > x) .

log.p

Logical; If TRUE, values are returned on the log scale.

p

Vector of probabilities.

n

Number of draws to sample from the distribution.

Details

The quantile function has no known closed form for this parameterization and is therefore computed numerically via inversion of the cumulative distribution function over the finite support 0:size.