hpois: Extension of the Hurdle Poisson Distribution

In countreg: Count Data Regression

Extension of the Hurdle Poisson Distribution

Description

Score function, hessian, mean, and, variance for the (zero-)hurdle Poisson distribution with parameters mu (= mean of the underlying Poisson distribution) and hurdle crossing probability pi (i.e., 1 - pi is the probability for observed zeros).

Usage

shpois(x, lambda, pi, parameter = c("lambda", "pi"), drop = TRUE)
hhpois(x, lambda, pi, parameter = c("lambda", "pi"), drop = TRUE)
mean_hpois(lambda, pi, drop = TRUE)
var_hpois(lambda, pi, drop = TRUE)

Arguments

x	vector of (positive integer) quantiles.
lambda	vector of non-negative means of the underlying Poisson distribution.
pi	vector of hurdle crossing probabilities (i.e., 1 - pi is the probability for observed zeros).
parameter	character. Should the derivative with respect to "lambda" 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 underlying Poisson distribution has density

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

for x = 0, 1, 2, \ldots. The hurdle density is then simply obtained as

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

for x = 1, 2, \ldots and g(0) = 1 - \pi, respectively.

Value

shpois gives the score function (= derivative of the log-density with respect to lambda and/or pi). hhpois gives the hessian (= 2nd derivative of the log-density with respect to lambda and/or pi). mean_hpois and var_hpois give the mean and the variance, respectively.

See Also

dhpois, dpois, hurdle

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