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