hnbinom: Extension of the Hurdle Negative Binomial Distribution

In countreg: Count Data Regression

Extension of the Hurdle Negative Binomial Distribution

Description

Score function, hessian, mean, and, variance for the (zero-)hurdle negative binomial distribution with parameters mu (= mean of the underlying negative binomial distribution), dispersion parameter theta (or equivalently size), and hurdle crossing probability pi (i.e., 1 - pi is the probability for observed zeros).

Usage

shnbinom(x, mu, theta, size, pi, parameter = c("mu", "theta", "pi"), drop = TRUE)
hhnbinom(x, mu, theta, size, pi, parameter = c("mu", "theta", "pi"), drop = TRUE)
mean_hnbinom(mu, theta, size, pi, drop = TRUE)
var_hnbinom(mu, theta, size, pi, drop = TRUE)

Arguments

x	vector of (positive integer) quantiles.
mu	vector of non-negative means of the underlying 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 hurdle crossing probabilities (i.e., 1 - pi is the probability for observed 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 underlying negative binomial distribution has density

f(x) = \frac{\Gamma(x + \theta)}{\Gamma(\theta) x!} \cdot \frac{\mu^y \theta^\theta}{(\mu + \theta)^{y + \theta}}

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

shnbinom gives the score function (= derivative of the log-density with respect to mu and/or theta and/or pi). hhnbinom gives the hessian (= 2nd derivative of the log-density with respect to mu and/or theta and/or pi). mean_hnbinom and var_hnbinom give the mean and the variance, respectively.

See Also

dhnbinom, dnbinom, hurdle

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