Extension of the Zero-Inflated Negative Binomial Distribution

Description

Score function for the zero-inflated negative binomial distribution with parameters mu (= mean of the uninflated distribution), dispersion parameter theta (or equivalently size), and inflation probability pi (for structural zeros).

Usage

szinbinom(x, mu, theta, size, pi, parameter = c("mu", "theta", "pi"), drop = TRUE)

Arguments

x	vector of (non-negative integer) quantiles.
mu	vector of non-negative means of the uninflated negative binomial distribution.
theta, size	vector of strictly positive dispersion parameters (shape parameter of the gamma mixing distribution). Only one of theta or size must be specified.
pi	vector of zero inflation probabilities for structural zeros.
parameter	character. Should the derivative with respect to “mu” and/or “theta” and/or “pi” be computed?
drop	logical. Should the result be a matrix (drop = FALSE) or should the dimension be dropped (drop = TRUE, the default)?

Details

The uninflated negative binomial distribution has density

f(x) =

for \(x = 0, 1, 2, \ldots\). The zero-inflated density is then simply obtained as

\(g(x) = \pi \cdot I_{\{0\}}(x) + (1 - \pi) \cdot f(x)\)

where \(I\) is the indicator function (for the point mass at zero).

Value

szinbinom gives the score function (= derivative of the log-density with respect to mu and/or theta and/or pi).

See Also

dzinbinom, dnbinom, zeroinfl