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Density function, distribution function, quantiles and random number generation for the skew-Laplace distribution.
dskewlap(x, Theta, logPars = FALSE)
pskewlap(q, Theta)
qskewlap(p, Theta)
rskewlap(n, Theta)
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.
Vector of quantiles.
Vector of probabilities.
Number of observations to be generated.
Vector of parameters of the skew-Laplace distribution:
.
Logical. If TRUE
the first and second components
of Theta are taken to be log(alpha) and log(beta) respectively.
David Scott d.scott@auckland.ac.nz, Ai-Wei Lee, Richard Trendall
The central skew-Laplace has mode zero, and is a mixture of a (negative)
exponential distribution with mean
The general skew-Laplace distribution is a shifted central skew-Laplace
distribution, where the mode is given by
The density is given by:
Fieller, N. J., Flenley, E. C. and Olbricht, W. (1992) Statistics of particle size data. Appl. Statist., 41, 127--146.
hyperbFitStart
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)
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