Vector of parameters of the skew-Laplace distribution:
mu, alpha and beta

.

logPars

Logical. If TRUE the second and third components
of param are taken to be log(alpha) and
log(beta) respectively.

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.

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

See Also

hyperbFitStart

Examples

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)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)
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Type 'demo()' for some demos, 'help()' for on-line help, or
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Type 'q()' to quit R.
> library(GeneralizedHyperbolic)
Loading required package: DistributionUtils
Loading required package: RUnit
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/GeneralizedHyperbolic/dskewlap.Rd_%03d_medium.png", width=480, height=480)
> ### Name: SkewLaplace
> ### Title: Skew-Laplace Distribution
> ### Aliases: dskewlap pskewlap qskewlap rskewlap
> ### Keywords: distribution
>
> ### ** Examples
>
> 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)
>
>
>
>
>
> dev.off()
null device
1
>