Log-likelihood of negative binomial model, for a fixed dispersion parameter

Given a unique dispersion parameter and a set of counts, together with a corresponding set of mean parameters, this function computes the sum of the log-probabilities of the counts under the NB model. The dispersion parameter is provided to the function through zeta = log(theta), where theta is sometimes called the inverse dispersion parameter.

Usage

nb.loglik.dispersion(zeta, Y, mu)

Arguments

zeta

a vector, the log of the inverse dispersion parameters of the negative binomial model

Y

a vector of counts

mu

a vector of mean parameters of the negative binomial

Value

the log-likelihood of the model.