Beta-Binomial Log-Likelihood

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

log_lik_beta_binom(
  x,
  size = 1,
  prob = 0.5,
  theta = 0,
  tlower = 0,
  tupper = Inf,
  memoize = FALSE
)

Arguments

x

A non-negative whole numeric vector of values.

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).

tlower

A numeric vector of the lower truncation point.

tupper

A numeric vector of the upper truncation point.

memoize

Whether or not to memoize the function.

Value

An numeric vector of the corresponding log-likelihoods.

See also

Other log_lik_dist: log_lik_bern(), log_lik_beta(), log_lik_binom(), log_lik_exp(), log_lik_gamma(), log_lik_gamma_pois(), log_lik_gamma_pois_zi(), log_lik_lnorm(), log_lik_neg_binom(), log_lik_norm(), log_lik_pois(), log_lik_pois_zi(), log_lik_skewnorm(), log_lik_student(), log_lik_unif()

Examples

log_lik_beta_binom(c(0, 1, 2), 3, 0.5, 0)
#> [1] -2.0794415 -0.9808293 -0.9808293