extraDistr (version 1.9.1)

NormalMix: Mixture of normal distributions

Description

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

Usage

dmixnorm(x, mean, sd, alpha, log = FALSE)
pmixnorm(q, mean, sd, alpha, lower.tail = TRUE, log.p = FALSE)
rmixnorm(n, mean, sd, alpha)

Arguments

x, q

vector of quantiles.

mean

matrix (or vector) of means.

sd

matrix (or vector) of standard deviations.

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 $$ f(x) = \alpha_1 f_1(x; \mu_1, \sigma_1) + \dots + \alpha_k f_k(x; \mu_k, \sigma_k) $$

Cumulative distribution function $$ F(x) = \alpha_1 F_1(x; \mu_1, \sigma_1) + \dots + \alpha_k F_k(x; \mu_k, \sigma_k) $$

where \(\sum_i \alpha_i = 1\).

Examples

x <- rmixnorm(1e5, c(0.5, 3, 6), c(3, 1, 1), c(1/3, 1/3, 1/3))
hist(x, 100, freq = FALSE)
curve(dmixnorm(x, c(0.5, 3, 6), c(3, 1, 1), c(1/3, 1/3, 1/3)),
      -20, 20, n = 500, col = "red", add = TRUE)
hist(pmixnorm(x, c(0.5, 3, 6), c(3, 1, 1), c(1/3, 1/3, 1/3)))
plot(ecdf(x))
curve(pmixnorm(x, c(0.5, 3, 6), c(3, 1, 1), c(1/3, 1/3, 1/3)),
      -20, 20, n = 500, col = "red", lwd = 2, add = TRUE)