extraDistr (version 1.8.1)

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, $P[X > x]$.

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)
xx <- seq(-1, 100, by = 0.01)
hist(x, 100, freq = FALSE)
lines(xx, dhnorm(xx, 2), col = "red")
hist(phnorm(x, 2))
plot(ecdf(x))
lines(xx, phnorm(xx, 2), col = "red", lwd = 2)