LaplacesDemon: dist.Log.Laplace – R documentation

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dist.Log.Laplace

Log-Laplace Distribution: Univariate Symmetric

Description

These functions provide the density, distribution function, quantile function, and random generation for the univariate, symmetric, log-Laplace distribution with location parameter location and scale parameter scale.

Usage

dllaplace(x, location=0, scale=1, log=FALSE)
pllaplace(q, location=0, scale=1)
qllaplace(p, location=0, scale=1)
rllaplace(n, location=0, scale=1)

Arguments

`x, q`	These are each a vector of quantiles.
`p`	This is a vector of probabilities.
`n`	This is the number of observations, which must be a positive integer that has length 1.
`location`	This is the location parameter mu.
`scale`	This is the scale parameter lambda, which must be positive.
`log`	Logical. If `log=TRUE`, then the logarithm of the density is returned.

Details

Application: Continuous Univariate
Density 1: p(theta) = ((sqrt(2)/lambda)^2 / (2*(sqrt(2)/lambda))) * exp(-(sqrt(2)/lambda)*(theta - mu)), theta >= exp(mu)
Density 2: p(theta) = ((sqrt(2)/lambda)^2 / (2*(sqrt(2)/lambda))) * exp((sqrt(2)/lambda)*(theta - mu)),theta < exp(mu)
Inventor: Pierre-Simon Laplace
Notation 1: theta ~ LL(mu, lambda)
Notation 2: p(theta) = LL(theta | mu, lambda)
Parameter 1: location parameter mu
Parameter 2: scale parameter lambda > 0
Mean: E(theta) =
Variance: var(theta) =
Mode: mode(theta) =

The univariate, symmetric log-Laplace distribution is derived from the Laplace distribution. Multivariate and asymmetric versions also exist.

These functions are similar to those in the VGAM package.

Value

dllaplace gives the density, pllaplace gives the distribution function, qllaplace gives the quantile function, and rllaplace generates random deviates.

References

Kozubowski, T. J. and Podgorski, K. (2003). "Log-Laplace Distributions". International Mathematical Journal, 3, p. 467–495.

Examples

library(LaplacesDemon)
x <- dllaplace(1,0,1)
x <- pllaplace(1,0,1)
x <- qllaplace(0.5,0,1)
x <- rllaplace(100,0,1)

#Plot Probability Functions
x <- seq(from=0.1, to=20, by=0.1)
plot(x, dllaplace(x,0,0.1), ylim=c(0,1), type="l", main="Probability Function",
     ylab="density", col="red")
lines(x, dllaplace(x,0,0.5), type="l", col="green")
lines(x, dllaplace(x,0,1.5), type="l", col="blue")
legend(2, 0.9, expression(paste(mu==0, ", ", lambda==0.1),
     paste(mu==0, ", ", lambda==0.5), paste(mu==0, ", ", lambda==1.5)),
     lty=c(1,1,1), col=c("red","green","blue"))

LaplacesDemon

Complete Environment for Bayesian Inference

v16.1.4

MIT + file LICENSE

Authors

Byron Hall [aut], Martina Hall [aut], Statisticat, LLC [aut], Eric Brown [ctb], Richard Hermanson [ctb], Emmanuel Charpentier [ctb], Daniel Heck [ctb], Stephane Laurent [ctb], Quentin F. Gronau [ctb], Henrik Singmann [cre]

Initial release