## Description

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

## Usage

 ```1 2 3 4 5 6 7``` ```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 ≤ 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 t distribution parametrized by degrees of freedom ν and scale σ, then |X| follows half-t distribution parametrized by degrees of freedom ν and scale σ.

## 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.

`HalfNormal`, `HalfCauchy`
 ```1 2 3 4 5 6``` ```x <- rht(1e5, 2, 2) hist(x, 500, freq = FALSE, xlim = c(0, 100)) curve(dht(x, 2, 2), 0, 100, col = "red", add = TRUE) hist(pht(x, 2, 2)) plot(ecdf(x), xlim = c(0, 100)) curve(pht(x, 2, 2), 0, 100, col = "red", lwd = 2, add = TRUE) ```