Log-likelihood of the negative binomial model Given a vector of counts, this function computes the sum of the log-probabilities of the counts under a negative binomial (NB) model. The NB distribution is parametrized by two parameters: the mean value and the dispersion of the negative binomial distribution

Log-likelihood of the negative binomial model Given a vector of counts, this function computes the sum of the log-probabilities of the counts under a negative binomial (NB) model. The NB distribution is parametrized by two parameters: the mean value and the dispersion of the negative binomial distribution

Usage

nb.loglik(Y, mu, theta)

Arguments

Y

the vector of counts

mu

the vector of mean parameters of the negative binomial

theta

the vector of dispersion parameters of the negative binomial, or a single scalar is also possible if the dispersion parameter is constant. Note that theta is sometimes called inverse dispersion parameter (and phi=1/theta is then called the dispersion parameter). We follow the convention that the variance of the NB variable with mean mu and dispersion theta is mu + mu^2/theta.

Value

the log-likelihood of the model.