Slash: Slash Distribution

Description

Density function, distribution function, and random generation for the slash distribution.

Usage

dslash(x, mu = 0, sigma = 1, log = FALSE, smallno = .Machine$double.eps*1000)
pslash(q, mu = 0, sigma = 1, very.negative = -10000)
rslash(n, mu = 0, sigma = 1)

Arguments

x, q

vector of quantiles.

Same as runif.

mu, sigma

the mean and standard deviation of the univariate normal distribution.

log

Logical. If TRUE then the logarithm of the density is returned.

very.negative

Numeric, of length 1. A large negative value. For (q-mu)/sigma values less than this, the value 0 is returned because integrate tends to fail. A warning is issued. Similarly,

smallno

See slash.

Value

dslash gives the density, and pslash gives the distribution function, rslash generates random deviates.

Details

See slash, the VGAM family function for estimating the two parameters by maximum likelihood estimation, for the formula of the probability density function and other details.

Function pslash uses a for () loop and integrate, meaning it's very slow. It may also be inaccurate for extreme values of q, and returns with 1 or 0 values when too extreme compared to very.negative.

Examples

Run this code

curve(dslash, col = "blue", ylab = "f(x)", -5, 5, ylim = c(0, 0.4), las = 1,
     main = "Standard slash, normal and Cauchy densities", lwd = 2)
curve(dnorm, col = "black", lty = 2, lwd = 2, add = TRUE)
curve(dcauchy, col = "orange", lty = 3, lwd = 2, add = TRUE)
legend("topleft", c("slash", "normal", "Cauchy"), lty = 1:3,
       col = c("blue","black","orange"), lwd = 2)

curve(pslash, col = "blue", -5, 5, ylim = 0:1)
pslash(c(-Inf, -20000, 20000, Inf))  # Gives a warning