dFBB function

Probability mass function of the flexible beta-binomial distribution

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

dFBB(x, size, mu, theta = NULL, phi = NULL, p, w)

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.
• p: the mixing weight. It must lie in (0, 1).
• w: the normalized distance among component means. It must lie in (0, 1).

Returns

A vector with the same length as x.

Details

The FBB distribution is a special mixture of two beta-binomial distributions with probability mass function

for $x \in \lbrace 0, 1, \dots, n \rbrace$, where $BB(x;\cdot,\cdot)$ is the beta-binomial distribution with a mean-precision parameterization. Moreover, $\phi=(1-\theta)/\theta>0$ is a precision parameter, $0<p<1$ is the mixing weight, $0<\mu=p\lambda_1+(1-p)\lambda_2<1$ is the overall mean, $0<w<1$ is the normalized distance between component means, and $\lambda_1=\mu+(1-p)w$ and $\lambda_2=\mu-pw$ are the scaled means of the first and second component of the mixture, respectively.

Examples

dFBB(x = c(5,7,8), size=10, mu = .3, phi = 20, p = .5, w = .5)

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