zipois: Extension of the Zero-Inflated Poisson Distribution

In countreg: Count Data Regression

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).

See Also

dzipois, dpois, zeroinfl

countreg documentation built on Dec. 4, 2023, 3:09 a.m.