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
.
dalaplace(x, location=0, scale=1, tau=0.5, kappa=sqrt(tau/(1-tau))) palaplace(q, location=0, scale=1, tau=0.5, kappa=sqrt(tau/(1-tau))) qalaplace(p, location=0, scale=1, tau=0.5, kappa=sqrt(tau/(1-tau))) ralaplace(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. Positive integer of length 1. |
location |
the location parameter xi. |
scale |
the scale parameter b. 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. |
There are several 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.
Apart from n
, all the above arguments may be vectors and
are recyled to the appropriate length if necessary.
dalaplace
gives the density,
palaplace
gives the distribution function,
qalaplace
gives the quantile function, and
ralaplace
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; b = 1.5; kappa = 2 ## Not run: plot(x, dalaplace(x, loc, b, 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="") abline(h=0, col="blue", lty=2) lines(qalaplace(seq(0.05,0.95,by=0.05), loc, b, kappa=kappa), dalaplace(qalaplace(seq(0.05,0.95,by=0.05), loc, b, kappa=kappa), loc, b, kappa=kappa), col="purple", lty=3, type="h") lines(x, palaplace(x, loc, b, kappa=kappa), type="l", col="red") abline(h=0, lty=2) ## End(Not run) palaplace(qalaplace(seq(0.05,0.95,by=0.05), loc, b, kappa=kappa), loc, b, kappa=kappa)