Skew-Laplace Distribution
Density function, distribution function, quantiles and random number generation for the skew-Laplace distribution.
dskewlap(x, mu = 0, alpha = 1, beta = 1,
param = c(mu, alpha, beta), logPars = FALSE)
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))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 |
.
logPars |
Logical. If |
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
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.
David Scott d.scott@auckland.ac.nz, Ai-Wei Lee, Richard Trendall
Fieller, N. J., Flenley, E. C. and Olbricht, W. (1992) Statistics of particle size data. Appl. Statist., 41, 127–146.
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")
DistributionUtils::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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.