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.
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).
See also
Other log_lik_dist:
log_lik_bern(),
log_lik_binom(),
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()
Examples
log_lik_beta_binom(c(0, 1, 2), 3, 0.5, 0)
#> [1] -2.0794415 -0.9808293 -0.9808293