alaplaceUC {VGAM} | R Documentation |
Density, distribution function, quantile function and random generation
for the 3-parameter asymmetric Laplace distribution with location
parameter location
, scale parameter scale
,
and asymmetry parameter kappa
.
dalap(x, location=0, scale=1, tau=0.5, kappa=sqrt(tau/(1-tau)), log=FALSE) palap(q, location=0, scale=1, tau=0.5, kappa=sqrt(tau/(1-tau))) qalap(p, location=0, scale=1, tau=0.5, kappa=sqrt(tau/(1-tau))) ralap(n, location=0, scale=1, tau=0.5, kappa=sqrt(tau/(1-tau)))
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations.
If length(n) > 1 then the length is taken to be the number required.
|
location |
the location parameter xi. |
scale |
the scale parameter sigma. Must consist of positive values. |
tau |
the quantile parameter tau.
Must consist of values in (0,1).
This argument is used to specify kappa and is ignored
if kappa is assigned.
|
kappa |
the asymmetry parameter kappa. Must consist of positive values. |
log |
if TRUE , probabilities p are given as log(p) .
|
There are many variants of asymmetric Laplace distributions (ALDs) and
this one is known as the ALD by Kotz et al. (2001).
See alaplace3
, the VGAM family function
for estimating the three parameters by maximum likelihood estimation,
for formulae and details.
dalap
gives the density,
palap
gives the distribution function,
qalap
gives the quantile function, and
ralap
generates random deviates.
T. W. Yee
Kotz, S., Kozubowski, T. J. and Podgorski, K. (2001) The Laplace distribution and generalizations: a revisit with applications to communications, economics, engineering, and finance, Boston: Birkhauser.
x = seq(-5, 5, by=0.01) loc = 0; sigma = 1.5; kappa = 2 ## Not run: plot(x, dalap(x, loc, sigma, kappa=kappa), type="l", col="blue", main="Blue is density, red is cumulative distribution function", ylim=c(0,1), sub="Purple are 5,10,...,95 percentiles", las=1, ylab="", cex.main=0.5) abline(h=0, col="blue", lty=2) lines(qalap(seq(0.05,0.95,by=0.05), loc, sigma, kappa=kappa), dalap(qalap(seq(0.05,0.95,by=0.05), loc, sigma, kappa=kappa), loc, sigma, kappa=kappa), col="purple", lty=3, type="h") lines(x, palap(x, loc, sigma, kappa=kappa), type="l", col="red") abline(h=0, lty=2) ## End(Not run) palap(qalap(seq(0.05,0.95,by=0.05), loc, sigma, kappa=kappa), loc, sigma, kappa=kappa)