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Folded normal distribution

foldnorm.Rd

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

Value

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

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.

See also

halft, halfcauchy

Examples

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