dztpois {distributions3} R Documentation

## The zero-truncated Poisson distribution

### Description

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.

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)



[Package distributions3 version 0.2.1 Index]