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The zero-truncated Poisson distribution

Source: R/ZTPoisson.R
ztpois.Rd

Density, distribution function, quantile function, and random generation for the zero-truncated Poisson distribution with parameter lambda.

Usage

dztpois(x, lambda, log = FALSE)

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

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

rztpois(n, lambda)

Arguments

x

vector of (non-negative integer) quantiles.

lambda

vector of (non-negative) Poisson parameters.

log, log.p

logical indicating whether probabilities p are given as log(p).

q

vector of quantiles.

lower.tail

logical indicating whether probabilities are \(P[X \le x]\) (lower tail) or \(P[X > x]\) (upper tail).

p

vector of probabilities.

n

number of random values to return.

Details

The Poisson distribution left-truncated at zero (or zero-truncated Poisson for short) is the distribution obtained, when considering a Poisson variable Y conditional on Y being greater than zero.

All functions follow the usual conventions of d/p/q/r functions in base R. In particular, all four ztpois functions for the zero-truncated Poisson distribution call the corresponding pois functions for the Poisson distribution from base R internally.

See also

ZTPoisson, dpois

Examples

## theoretical probabilities for a zero-truncated Poisson distribution
x <- 0:8
p <- dztpois(x, lambda = 2.5)
plot(x, p, type = "h", lwd = 2)


## corresponding empirical frequencies from a simulated sample
set.seed(0)
y <- rztpois(500, lambda = 2.5)
hist(y, breaks = -1:max(y) + 0.5)