## Description

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

## Usage

 ```1 2 3 4 5 6 7``` ```dhcauchy(x, sigma = 1, log = FALSE) phcauchy(q, sigma = 1, lower.tail = TRUE, log.p = FALSE) qhcauchy(p, sigma = 1, lower.tail = TRUE, log.p = FALSE) rhcauchy(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 ≤ 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 Cauchy centered at 0 and parametrized by scale σ, then |X| follows half-Cauchy distribution parametrized by scale σ. Half-Cauchy distribution is a special case of half-t distribution with ν=1 degrees of freedom.

## 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.

`HalfT`
 ```1 2 3 4 5 6``` ```x <- rhcauchy(1e5, 2) hist(x, 2e5, freq = FALSE, xlim = c(0, 100)) curve(dhcauchy(x, 2), 0, 100, col = "red", add = TRUE) hist(phcauchy(x, 2)) plot(ecdf(x), xlim = c(0, 100)) curve(phcauchy(x, 2), col = "red", lwd = 2, add = TRUE) ```