Probability Mass Function of the Hurdle Poisson Distribution

Computes the probability density (or log-density) for the Poisson hurdle distribution. This distribution combines a point mass at zero with a truncated-at-zero Poisson distribution for positive counts.

Usage

dhurdlepois(y, lambda, pi, log = FALSE)

Arguments

y: Numeric vector of observed counts.
lambda: Numeric vector of Poisson mean parameters (must be positive).
pi: Numeric vector of hurdle probabilities (probability of structural zeros), where each value must be between 0 and 1.
log: Logical; if TRUE, probabilities are returned on the log scale.

Value

A numeric vector of the same length as y, giving the density (or log-density) of the Poisson hurdle distribution.

Details

The hurdle Poisson distribution assumes: $$ P(Y = 0) = \pi $$ and for $y > 0$: $$ P(Y = y) = (1 - \pi) \frac{P_{\text{Pois}}(Y = y)}{1 - P_{\text{Pois}}(Y = 0)} $$ where $P_{\text{Pois}}(Y = y)$ is the standard Poisson probability mass function.

The function is vectorized over all parameters.

Examples

# Example usage:
y <- 0:5
lambda <- 2
pi <- 0.3
dhurdlepois(y, lambda, pi)
#> [1] 0.30000000 0.21912470 0.21912470 0.14608313 0.07304157 0.02921663
dhurdlepois(y, lambda, pi, log = TRUE)
#> [1] -1.203973 -1.518114 -1.518114 -1.923579 -2.616727 -3.533017