Distribution and quantile functions of a one-dimensional mixture

The exact cumulative distribution function \(F(x) = \sum_k w_k \Phi\!\left((x - \mu_k) / \sigma_k\right)\) of a one-dimensional Gaussian mixture, and its inverse by monotone root-finding. Together with dgmm() and rgmm() these complete the usual d/p/q/r quartet for the one-dimensional case; for tail probabilities of a multivariate mixture, marginalise first (gmm_marginalise()) or push through the relevant linear functional (gmm_affine()).

Usage

pgmm(q, g, lower.tail = TRUE)

qgmm(p, g)

Arguments

q

Numeric vector of quantiles.

g

A one-dimensional gmm (or gmm_fit).

lower.tail

Logical; if TRUE (default), probabilities are \(P(X \le x)\).

p

Numeric vector of probabilities in (0, 1).

Value

A numeric vector the length of the first argument.

See also

Other ops: dgmm(), gmm_canonicalise(), gmm_conditionalise(), gmm_divergence(), gmm_kld(), gmm_marginalise(), gmm_mean(), gmm_modes(), rgmm()

Examples

g <- gmm(weights = c(0.4, 0.6), means = list(-2, 1),
         covariances = list(matrix(0.5), matrix(1)))
pgmm(c(-2, 0, 2), g)
#> [1] 0.2008099 0.4942576 0.9048068
qgmm(c(0.1, 0.5, 0.9), g)
#> [1] -2.47778037  0.03783803  1.96742159