The Truncated Poisson Distribution

Density, distribution function, quantile function, and random generation for the truncated Poisson distribution with parameter lambda, truncated to the interval (lower, upper].

Usage

dtpois(x, lambda, lower, upper, log = FALSE)

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

qtpois(p, lambda, lower, upper, lower.tail = TRUE, log.p = FALSE)

rtpois(n, lambda, lower, upper)

Arguments

x: vector of (non-negative integer) quantiles.
lambda: vector of (non-negative) Poisson means.
lower: vector of lower truncation bounds (exclusive).
upper: vector of upper truncation bounds (inclusive).
log: logical; if TRUE, probabilities p are given as log(p).
q: vector of quantiles.
lower.tail: logical; if TRUE (default), probabilities are $P[X \le x]$, otherwise, $P[X > x]$.
log.p: logical; if TRUE, probabilities p are given as log(p).
p: vector of probabilities.
n: number of observations. If length(n) > 1, the length is taken to be the number required.

Value

dtpois gives the density.

ptpois gives the distribution function.

qtpois gives the quantile function.

rtpois generates random deviates.

Details

The truncated Poisson distribution has density $$f(x) = \frac{P(X = x)}{P(a < X \le b)}$$ for $x \in \{a+1, a+2, \ldots, b\}$, where $X \sim \text{Poisson}(\lambda)$, $a$ is the lower bound and $b$ is the upper bound.

Examples