hskewlaplace {event}

Log Hazard Function for a Skew Laplace Process

Description

These functions provide information about the skew Laplace distribution with location parameter equal to m, dispersion equal to s, and skew equal to f: log hazard. (See 'rmutil' for the d/p/q/r boxcox functions density, cumulative distribution, quantiles, and random generation). For f=1, this is an ordinary (symmetric) Laplace distribution.

The skew Laplace distribution has density

f(y) = \frac{\nu\exp(-\nu(y-\mu)/\sigma)}{(1+\nu^2)\sigma}

if y\ge\mu and else

f(y) = \frac{\nu\exp((y-\mu)/(\nu\sigma))}{(1+\nu^2)\sigma}

where \mu is the location parameter of the distribution, \sigma is the dispersion, and \nu is the skew.

The mean is given by \mu+\frac{\sigma(1-\nu^2)}{\sqrt{2}\nu} and the variance by \frac{\sigma^2(1+\nu^4)}{2\nu^2}.

Note that this parametrization of the skew (family) parameter is different than that used for the multivariate skew Laplace distribution in 'growth::elliptic'.

Usage

hskewlaplace(y, m=0, s=1, f=1)

Arguments

y

vector of responses.

m

vector of location parameters.

s

vector of dispersion parameters.

f

vector of skew parameters.

Author(s)

J.K. Lindsey

See Also

dexp for the exponential distribution, dcauchy for the Cauchy distribution, and dlaplace for the Laplace distribution.

Examples

hskewlaplace(5, 2, 1, 0.5)