HalfT function

Half-t distribution

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

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, $P[X > x]$.

• 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 $\nu$

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

Examples

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)

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

HalfNormal, HalfCauchy