foldnorm: Folded normal distribution

In RTMBdist: Distributions Compatible with Automatic Differentiation by 'RTMB'

Folded normal distribution

Description

Density, distribution function, and random generation for the folded normal distribution.

Usage

dfoldnorm(x, mu = 0, sigma = 1, log = FALSE)

pfoldnorm(q, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE)

rfoldnorm(n, mu = 0, sigma = 1)

Arguments

x, q	vector of quantiles
mu	location parameter
sigma	scale parameter, must be positive.
log, log.p	logical; if TRUE, probabilities/ densities p are returned as \log(p).
lower.tail	logical; if TRUE, probabilities are P[X \le x], otherwise, P[X > x].
n	number of random values to return
p	vector of probabilities

Details

This implementation of dfoldnorm allows for automatic differentiation with RTMB.

f(x;\,\mu,\sigma) = \frac{1}{\sigma\sqrt{2\pi}}\left[\exp\!\left(-\frac{(x-\mu)^2}{2\sigma^2}\right) + \exp\!\left(-\frac{(x+\mu)^2}{2\sigma^2}\right)\right], \quad x \geq 0.

With \mu = 0 this is the half-normal distribution, the limiting case of the half-t as its degrees of freedom grow.

Value

dfoldnorm gives the density, pfoldnorm gives the distribution function, and rfoldnorm generates random deviates.

See Also

halft, halfcauchy

Examples

x <- rfoldnorm(1, 1, 2)
d <- dfoldnorm(x, 1, 2)
p <- pfoldnorm(x, 1, 2)

RTMBdist documentation built on Oct. 31, 2026, 5:07 p.m.