HalfNormal: 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, \(P[X > x]\).

vector of probabilities.

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.

Examples

Run this code

# NOT RUN {
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)

# }