modelSelection (version 1.0.5)

dalapl: Density and random draws from the asymmetric Laplace distribution

Description

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

Usage

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)

Value

dalapl returns the density function,

palapl the cumulative probability,

ralapl random draws.

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

Author

David Rossell

Details

For x<=th the asymmetric Laplace pdf is

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

and for x>th it is

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

Examples

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)