dalapl function

Density and random draws from the asymmetric Laplace distribution

dalapl evaluates the probability density function, palapl the cumulative probability function and ralapl generates random draws.

dalapl(x, th=0, scale=1, alpha=0, logscale=FALSE)

palapl(x, th=0, scale=1, alpha=0)

ralapl(n, th=0, scale=1, alpha=0)

Arguments

• x: Vector of values at which to evaluate the pdf/cdf
• n: Number of random draws
• th: Location parameter (mode)
• scale: Scale parameter (proportional to variance)
• alpha: Asymmetry parameter, must be between -1 and 1
• logscale: If TRUE the log-pdf is returned

Details

For x<=th the asymmetric Laplace pdf is

0.5exp(-abs(th-x)/(sqrt(scale)(1+alpha)))/sqrt(scale)

and for x>th it is

0.5exp(-abs(th-x)/(sqrt(scale)(1-alpha)))/sqrt(scale)

Returns

dalapl returns the density function, palapl the cumulative probability, ralapl random draws.

Author(s)

David Rossell

Examples

library(mombf)
e <- ralapl(n=10^4, th=1, scale=2, alpha=0.5)
thseq <- seq(min(e),max(e),length=1000)
hist(e, main='', breaks=30, prob=TRUE)
lines(thseq, dalapl(thseq, th=1, scale=2, alpha=0.5), col=2)