HalfNormal {extraDistr}

Half-normal distribution

Description

Density, distribution function, quantile function and random generation for the half-normal distribution.

Usage

dhnorm(x, sigma = 1, log = FALSE)

phnorm(q, sigma = 1, lower.tail = TRUE, log.p = FALSE)

qhnorm(p, sigma = 1, lower.tail = TRUE, log.p = FALSE)

rhnorm(n, sigma = 1)

Arguments

x, q

vector of quantiles.

sigma

positive valued scale parameter.

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].

p

vector of probabilities.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

Details

If X follows normal distribution centered at 0 and parametrized by scale \sigma, then |X| follows half-normal distribution parametrized by scale \sigma. Half-t distribution with \nu=\infty degrees of freedom converges to half-normal distribution.

References

Gelman, A. (2006). Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper). Bayesian analysis, 1(3), 515-534.

Jacob, E. and Jayakumar, K. (2012). On Half-Cauchy Distribution and Process. International Journal of Statistika and Mathematika, 3(2), 77-81.

See Also

HalfT

Examples

x <- rhnorm(1e5, 2)
hist(x, 100, freq = FALSE)
curve(dhnorm(x, 2), 0, 8, col = "red", add = TRUE)
hist(phnorm(x, 2))
plot(ecdf(x))
curve(phnorm(x, 2), 0, 8, col = "red", lwd = 2, add = TRUE)