Beta-Binomial Deviances

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.

dev_beta_binom(x, size = 1, prob = 0.5, theta = 0, res = 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).

res

A flag specifying whether to return the deviance residual as opposed to the deviance.

Value

An numeric vector of the corresponding deviances or deviance residuals.

See also

Other dev_dist: dev_bern(), dev_binom(), dev_gamma_pois(), dev_gamma(), dev_lnorm(), dev_neg_binom(), dev_norm(), dev_pois_zi(), dev_pois(), dev_skewnorm(), dev_student()

Examples

dev_beta_binom(c(0, 1, 2), 1, 0.5, 0)
#> Warning: NA/Inf replaced by maximum positive value
#> Warning: NA/Inf replaced by maximum positive value
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#> Warning: NaNs produced
#> [1] 1.386294 1.386294      NaN