Hurdle geometric distribution

Probability mass function, distribution function, and random generation for the hurdle (zero-altered) geometric distribution.

Usage

dhgeom(x, prob, zeroprob = 0.5, log = FALSE)

phgeom(q, prob, zeroprob = 0.5, lower.tail = TRUE, log.p = FALSE)

rhgeom(n, prob, zeroprob = 0.5)

Arguments

x, q: integer vector of counts
prob: probability of success in each trial, in (0,1)
zeroprob: probability of a zero, between 0 and 1
log, log.p: logical; return log-density if TRUE
lower.tail: logical; if TRUE, probabilities are $P[X \le x]$, otherwise, $P[X > x]$.
n: number of random values to return.

Value

dhgeom gives the probability mass function, phgeom gives the distribution function, and rhgeom generates random deviates.

Details

This implementation allows for automatic differentiation with RTMB.

A hurdle distribution models the zeros and the positive counts as two separate processes: the probability of a zero is a free parameter, and the positive counts follow the corresponding zero-truncated distribution. Writing $p_0$ for zeroprob, $$P(X = 0) = p_0, \qquad P(X = x) = (1 - p_0)\,\frac{P_{\mathrm{Geom}}(x;\,\pi)}{1 - \pi_0}, \quad x = 1, 2, \ldots$$ where $\pi_0 = P_{\mathrm{Geom}}(0;\,\pi) = \pi$ is the probability of a zero under the ordinary geometric.

Unlike zero-inflation, which can only add zeros to those the geometric already produces, zeroprob here is exactly the probability of a zero and may be larger or smaller than $\pi_0$. The two coincide with the ordinary geometric when zeroprob equals $\pi_0$.

References

Mullahy, J. (1986) Specification and testing of some modified count data models. Journal of Econometrics, 33, 341-365.

Examples

set.seed(123)
x <- rhgeom(5, prob = 0.3, zeroprob = 0.4)
d <- dhgeom(x, prob = 0.3, zeroprob = 0.4)
p <- phgeom(x, prob = 0.3, zeroprob = 0.4)