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).
- res
A flag specifying whether to return the deviance residual as opposed to the deviance.
See also
Other dev_dist:
dev_bern(),
dev_binom(),
dev_gamma(),
dev_gamma_pois(),
dev_lnorm(),
dev_neg_binom(),
dev_norm(),
dev_pois(),
dev_pois_zi(),
dev_skewnorm(),
dev_student()
Examples
dev_beta_binom(c(0, 1, 2), 10, 0.5, 0.1)
#> [1] 10.758196 5.136943 2.608386