countreg

Extension of the Zero-Inflated Poisson Distribution

Description

Score function for the zero-inflated Poisson distribution with parameters lambda (= mean of the uninflated distribution) and inflation probability pi (for structural zeros).

Usage

szipois(x, lambda, pi, parameter = c("lambda", "pi"), drop = TRUE)

Arguments

`x`	vector of (non-negative integer) quantiles.
`lambda`	vector of non-negative means of the uninflated Poisson distribution.
`pi`	vector of zero inflation probabilities for structural zeros.
`parameter`	character. Should the derivative with respect to `“mu”` and/or `“size”` 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 Poisson distribution has density

\(f(x) = \frac{\lambda^x e^{-\lambda}}{x!}\)

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

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