Description Usage Arguments Details Value Author(s) References See Also Examples
Density function, distribution function, quantiles and random number generation for the skewLaplace distribution.
1 2 3 4 5 6 7 8 
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 skewLaplace distribution: mu, alpha and beta 
.
The central skewLaplace 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 skewLaplace distribution is a shifted central skewLaplace 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 skewLaplace as a mixture of exponential observations.
David Scott [email protected], AiWei Lee, Richard Trendall
Fieller, N. J., Flenley, E. C. and Olbricht, W. (1992) Statistics of particle size data. Appl. Statist., 41, 127–146.
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 SkewLaplace Distribution")
curve(pskewlap(x, param = param), from = 5, to = 8, n = 1000)
title("Distribution Function of the\n SkewLaplace 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 SkewLaplace Distribution")
logHist(dataVector, main =
"LogDensity and LogHistogram\n of the SkewLaplace Distribution")
curve(log(dskewlap(x, param = param)), add = TRUE,
range(dataVector)[1], range(dataVector)[2], n = 500)

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