Vector of parameters of the skew-Laplace distribution:
alpha, beta and mu
.
logPars
Logical. If TRUE the first and second components
of Theta 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
Theta <- c(1,2,1)
par(mfrow = c(1,2))
curve(dskewlap(x, Theta), from = -5, to = 8, n = 1000)
title("Density of the\n Skew-Laplace Distribution")
curve(pskewlap(x, Theta), from = -5, to = 8, n = 1000)
title("Distribution Function of the\n Skew-Laplace Distribution")
dataVector <- rskewlap(500, Theta)
curve(dskewlap(x, Theta), 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, Theta)), 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)
R is free software and comes with ABSOLUTELY NO WARRANTY.
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Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.
Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
> library(HyperbolicDist)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/HyperbolicDist/dskewlap.Rd_%03d_medium.png", width=480, height=480)
> ### Name: SkewLaplace
> ### Title: Skew-Laplace Distribution
> ### Aliases: dskewlap pskewlap qskewlap rskewlap
> ### Keywords: distribution
>
> ### ** Examples
>
> Theta <- c(1,2,1)
> par(mfrow = c(1,2))
> curve(dskewlap(x, Theta), from = -5, to = 8, n = 1000)
> title("Density of the\n Skew-Laplace Distribution")
> curve(pskewlap(x, Theta), from = -5, to = 8, n = 1000)
> title("Distribution Function of the\n Skew-Laplace Distribution")
> dataVector <- rskewlap(500, Theta)
> curve(dskewlap(x, Theta), 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, Theta)), add = TRUE,
+ range(dataVector)[1], range(dataVector)[2], n = 500)
>
>
>
>
>
> dev.off()
null device
1
>