dBetaBin: Probability mass function of the beta-binomial distribution

In FlexReg: Regression Models for Bounded Continuous and Discrete Responses

Probability mass function of the beta-binomial distribution

Description

The function computes the probability mass function of the beta-binomial distribution.

Usage

dBetaBin(x, size, mu, theta = NULL, phi = NULL)

Arguments

x	a vector of quantiles.
size	the total number of trials.
mu	the mean parameter. It must lie in (0, 1).
theta	the overdispersion parameter. It must lie in (0, 1).
phi	the precision parameter, an alternative way to specify the overdispersion parameter theta. It must be a real positive value.

Details

The beta-binomial distribution has probability mass function

f_{BB}(x;\mu,\phi)={n\choose x} \frac{\Gamma{(\phi)}}{\Gamma{(\mu\phi)}\Gamma{((1-\mu)\phi)}} \frac{\Gamma{(\mu\phi+x)}\Gamma{((1-\mu)\phi + n - x)}}{\Gamma{(\phi + n)}},

for x \in \lbrace 0, 1, \dots, n \rbrace, where 0<\mu<1 identifies the mean and \phi=(1-\theta)/\theta >0 is the precision parameter.

Value

A vector with the same length as x.

References

Ascari, R., Migliorati, S. (2021). A new regression model for overdispersed binomial data accounting for outliers and an excess of zeros. Statistics in Medicine, 40(17), 3895–3914. doi:10.1002/sim.9005

Examples

dBetaBin(x = 5, size = 10, mu = .3, phi = 10)

FlexReg documentation built on Sept. 29, 2023, 9:06 a.m.