Zero-truncated Poisson distribution

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

Usage

dztpois(x, lambda, log = FALSE)

pztpois(q, lambda, lower.tail = TRUE, log.p = FALSE)

rztpois(n, lambda)

Arguments

x, q

integer vector of counts

lambda

vector of (non-negative) means

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

dztpois gives the probability mass function, pztpois gives the distribution function, and rztpois 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.

Examples

set.seed(123)
x <- rztpois(1, 0.5)
d <- dztpois(x, 0.5)
p <- pztpois(x, 0.5)