HalfT: Half-t distribution

Description

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

Usage

dht(x, nu, sigma = 1, log = FALSE)
pht(q, nu, sigma = 1, lower.tail = TRUE, log.p = FALSE)
qht(p, nu, sigma = 1, lower.tail = TRUE, log.p = FALSE)
rht(n, nu, sigma = 1)

Arguments

x, q

vector of quantiles.

nu, sigma

positive valued degrees of freedom and scale parameters.

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 t distribution parametrized by degrees of freedom $\nu$ and scale $\sigma$, then $|X|$ follows half-t distribution parametrized by degrees of freedom $\nu$ and scale $\sigma$.

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


x <- rht(1e5, 2, 2)
xx <- seq(-1, 100, by = 0.01)
hist(x, 500, freq = FALSE, xlim = c(0, 100))
lines(xx, dht(xx, 2, 2), col = "red")
hist(pht(x, 2, 2))
plot(ecdf(x), xlim = c(0, 100))
lines(xx, pht(xx, 2, 2), col = "red", lwd = 2)