The function computes the probability mass function of the beta-binomial distribution.
Usage
dBetaBin(x, size, mu, theta = NULL, phi = NULL)
Value
A vector with the same length as x.
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. It is an alternative way to specify the theta parameter. It must be a positive real value.
Details
The beta-binomial distribution has probability mass function
$${n\choose y} \frac{\Gamma{(\phi)}}{\Gamma{(\mu\phi)}\Gamma{((1-\mu)\phi)}} \frac{\Gamma{(\mu\phi+y)}\Gamma{((1-\mu)\phi + n - y)}}{\Gamma{(\phi + n)}},$$
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.
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