Zero-truncated geometric distribution

Probability mass function, distribution function, and random generation for the zero-truncated geometric distribution.

Usage

dztgeom(x, prob, log = FALSE)

pztgeom(q, prob, lower.tail = TRUE, log.p = FALSE)

rztgeom(n, prob)

Arguments

x, q: integer vector of counts
prob: probability of success in each trial, in (0,1)
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

dztgeom gives the probability mass function, pztgeom gives the distribution function, and rztgeom generates random deviates.

Details

This implementation allows for automatic differentiation with RTMB.

By definition, this distribution only has support on the positive integers (1, 2, ...). Any zero-truncated distribution is defined as $$P(X=x | X>0) = P(X=x) / (1 - P(X=0)),$$ where $P(X=x)$ is the probability mass function of the corresponding untruncated distribution. For the geometric with success probability $\pi$ this gives $$P(X=x | X>0) = \pi\,(1-\pi)^{x-1}, \quad x = 1, 2, \ldots$$

Examples

set.seed(123)
x <- rztgeom(5, prob = 0.3)
d <- dztgeom(x, prob = 0.3)
p <- pztgeom(x, prob = 0.3)