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)
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 |
p |
vector of probabilities. |
Probability density function
f(x) = α[1] * f1(x; λ[1]) + … + α[k] * fk(x; λ[k])
Cumulative distribution function
F(x) = α[1] * F1(x; λ[1]) + … + α[k] * Fk(x; λ[k])
where sum(α[i]) == 1.
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)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.