Slash function

Slash distribution

Probability mass function, distribution function and random generation for slash distribution.

dslash(x, mu = 0, sigma = 1, log = FALSE)

pslash(q, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE)

rslash(n, mu = 0, sigma = 1)

Arguments

• x, q: vector of quantiles.

• mu: vector of locations

• sigma: vector of positive valued 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, $P[X > x]$.

• n: number of observations. If length(n) > 1, the length is taken to be the number required.

Details

If $Z ~ Normal(0, 1)$ and $U ~ Uniform(0, 1)$, then $Z/U$ follows slash distribution.

Probability density function

Cumulative distribution function

Examples

x <- rslash(1e5, 5, 3)
hist(x, 1e5, freq = FALSE, xlim = c(-100, 100))
curve(dslash(x, 5, 3), -100, 100, col = "red", n = 500, add = TRUE)
hist(pslash(x, 5, 3))
plot(ecdf(x), xlim = c(-100, 100))
curve(pslash(x, 5, 3), -100, 100, col = "red", lwd = 2, n = 500, add = TRUE)