# SkewLaplace: Skew Laplace Distribution In rmutil: Utilities for Nonlinear Regression and Repeated Measurements Models

 SkewLaplace R Documentation

## Skew Laplace Distribution

### 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`: density, cumulative distribution, quantiles, log hazard, and random generation. For `f=1`, this is an ordinary (symmetric) Laplace distribution.

The skew Laplace distribution has density

f(y) = f*exp(-f*(y-m)/s)/((1+f^2)*s)

if y>=m and else

f(y) = f*exp((y-m)/(f*s))/((1+f^2)*s)

where m is the location parameter of the distribution, s is the dispersion, and f is the skew.

The mean is given by m + (s * (1 - f^2)) / (sqrt(2) * f) and the variance by (s^2 * (1 + f^4)) / (2 * f^2).

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

### Usage

```dskewlaplace(y, m=0, s=1, f=1, log=FALSE)
pskewlaplace(q, m=0, s=1, f=1)
qskewlaplace(p, m=0, s=1, f=1)
rskewlaplace(n, m=0, s=1, f=1)
```

### Arguments

 `y` vector of responses. `q` vector of quantiles. `p` vector of probabilities `n` number of values to generate `m` vector of location parameters. `s` vector of dispersion parameters. `f` vector of skew parameters. `log` if TRUE, log probabilities are supplied.

### Author(s)

J.K. Lindsey

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

### Examples

```dskewlaplace(5, 2, 1, 0.5)
pskewlaplace(5, 2, 1, 0.5)
qskewlaplace(0.95, 2, 1, 0.5)
rskewlaplace(10, 2, 1, 0.5)
```

rmutil documentation built on March 18, 2022, 6:55 p.m.