NormalMix: Mixture of normal distributions

In extraDistr: Additional Univariate and Multivariate Distributions

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)

extraDistr documentation built on May 29, 2024, 9:31 a.m.