# PoissonMix: Mixture of Poisson distributions In extraDistr: Additional Univariate and Multivariate Distributions

## Description

Density, distribution function and random generation for the mixture of Poisson distributions.

## Usage

 ```1 2 3 4 5``` ```dmixpois(x, lambda, alpha, log = FALSE) pmixpois(q, lambda, alpha, lower.tail = TRUE, log.p = FALSE) rmixpois(n, lambda, alpha) ```

## Arguments

 `x, q` vector of quantiles. `lambda` matrix (or vector) of (non-negative) means. `alpha` matrix (or vector) of mixing proportions; mixing proportions need to sum up to 1. `log, log.p` logical; if TRUE, probabilities p are given as log(p). `lower.tail` logical; if TRUE (default), probabilities are P[X ≤ x] otherwise, P[X > x]. `n` number of observations. If `length(n) > 1`, the length is taken to be the number required. `p` vector of probabilities.

## Details

Probability density function

f(x) = α * f1(x; λ) + … + α[k] * fk(x; λ[k])

Cumulative distribution function

F(x) = α * F1(x; λ) + … + α[k] * Fk(x; λ[k])

where sum(α[i]) == 1.

## Examples

 ```1 2 3 4 5 6 7 8 9``` ```x <- rmixpois(1e5, c(5, 12, 19), c(1/3, 1/3, 1/3)) xx <- seq(-1, 50) plot(prop.table(table(x))) lines(xx, dmixpois(xx, c(5, 12, 19), c(1/3, 1/3, 1/3)), col = "red") hist(pmixpois(x, c(5, 12, 19), c(1/3, 1/3, 1/3))) xx <- seq(0, 50, by = 0.01) plot(ecdf(x)) lines(xx, pmixpois(xx, c(5, 12, 19), c(1/3, 1/3, 1/3)), col = "red", lwd = 2) ```

extraDistr documentation built on Sept. 7, 2020, 5:09 p.m.