# Slash: Slash distribution In extraDistr: Additional Univariate and Multivariate Distributions

## Description

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

## Usage

 ```1 2 3 4 5``` ```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 ≤ 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

f(x) = [if x != 0:] (φ(0)-φ(x))/x^2 [else:] 1/(2*sqrt(2*π))

Cumulative distribution function

F(x) = [if x != 0:] Φ(x) - [φ(0)-φ(x)]/x [else:] 1/2

## Examples

 ```1 2 3 4 5 6``` ```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) ```

extraDistr documentation built on Sept. 7, 2020, 5:09 p.m.