PoissonMix function

Mixture of Poisson distributions

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

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 $P[X \le x]$

  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

Cumulative distribution function

where $sum(\alpha[i]) == 1$.

Examples

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)