dBetaBin function

Probability mass function of the beta-binomial distribution

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

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.

Returns

A vector with the same length as x.

Details

The beta-binomial distribution has probability mass function

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.

Examples

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

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