NormalMix function

Mixture of normal distributions

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

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

Cumulative distribution function

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

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)