Beta-Binomial Cumulative Distribution Function

This parameterization of the beta-binomial distribution uses an expected probability parameter, prob, and a dispersion parameter, theta. The parameters of the underlying beta mixture are alpha = (2 * prob) / theta and beta = (2 * (1 - prob)) / theta. This parameterization of theta is unconventional, but has useful properties when modelling. When theta = 0, the beta-binomial reverts to the binomial distribution. When theta = 1 and prob = 0.5, the parameters of the beta distribution become alpha = 1 and beta = 1, which correspond to a uniform distribution for the beta-binomial probability parameter.

Usage

prob_beta_binom(x, size = 1, prob = 0.5, theta = 0)

Arguments

x

A numeric vector of quantiles.

size

A non-negative whole numeric vector of the number of trials.

prob

A numeric vector of values between 0 and 1 of the probability of success.

theta

A non-negative numeric vector of the dispersion for the mixture models (student, gamma-Poisson and beta-binomial).

Value

An numeric vector of the corresponding probabilities.

See also

Other prob_dist: prob_bern(), prob_beta(), prob_binom(), prob_exp(), prob_gamma(), prob_gamma_pois(), prob_gamma_pois_zi(), prob_lnorm(), prob_neg_binom(), prob_norm(), prob_pois(), prob_pois_zi(), prob_skewnorm(), prob_student(), prob_unif()

Examples

prob_beta_binom(c(0, 1, 2), 3, 0.5, 0)
#> [1] 0.125 0.500 0.875