HalfNormal function

Half-normal distribution

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

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.

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)

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