# dskewlap: Skew-Laplace Distribution In sjp/GeneralizedHyperbolic: The generalized hyperbolic distribution

## Description

Density function, distribution function, quantiles and random number generation for the skew-Laplace distribution.

## Usage

 ```1 2 3 4 5 6 7 8``` ```dskewlap(x, mu = 0, alpha = 1, beta = 1, param = c(mu, alpha, beta)) pskewlap(q, mu = 0, alpha = 1, beta = 1, param = c(mu, alpha, beta)) qskewlap(p, mu = 0, alpha = 1, beta = 1, param = c(mu, alpha, beta)) rskewlap(n, mu = 0, alpha = 1, beta = 1, param = c(mu, alpha, beta)) ```

## Arguments

 `x, q` Vector of quantiles. `p` Vector of probabilities. `n` Number of observations to be generated. `mu` The location parameter, set to 0 by default. `alpha, beta` The shape parameters, both set to 1 by default. `param` Vector of parameters of the skew-Laplace distribution: mu, alpha and beta

.

## Details

The central skew-Laplace has mode zero, and is a mixture of a (negative) exponential distribution with mean beta, and the negative of an exponential distribution with mean alpha. The weights of the positive and negative components are proportional to their means.

The general skew-Laplace distribution is a shifted central skew-Laplace distribution, where the mode is given by mu.

The density is given by:

f(x)=(1/(alpha+beta)) e^((x - mu)/alpha)

for x <= mu, and

f(x)=(1/(alpha+beta)) e^(-(x - mu)/beta)

for x >= mu

## Value

`dskewlap` gives the density, `pskewlap` gives the distribution function, `qskewlap` gives the quantile function and `rskewlap` generates random variates. The distribution function is obtained by elementary integration of the density function. Random variates are generated from exponential observations using the characterization of the skew-Laplace as a mixture of exponential observations.

## Author(s)

David Scott [email protected], Ai-Wei Lee, Richard Trendall

## References

Fieller, N. J., Flenley, E. C. and Olbricht, W. (1992) Statistics of particle size data. Appl. Statist., 41, 127–146.

`hyperbFitStart`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```param <- c(1, 1, 2) par(mfrow = c(1, 2)) curve(dskewlap(x, param = param), from = -5, to = 8, n = 1000) title("Density of the\n Skew-Laplace Distribution") curve(pskewlap(x, param = param), from = -5, to = 8, n = 1000) title("Distribution Function of the\n Skew-Laplace Distribution") dataVector <- rskewlap(500, param = param) curve(dskewlap(x, param = param), range(dataVector)[1], range(dataVector)[2], n = 500) hist(dataVector, freq = FALSE, add = TRUE) title("Density and Histogram\n of the Skew-Laplace Distribution") logHist(dataVector, main = "Log-Density and Log-Histogram\n of the Skew-Laplace Distribution") curve(log(dskewlap(x, param = param)), add = TRUE, range(dataVector)[1], range(dataVector)[2], n = 500) ```