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)
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 |
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
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)
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