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)), lower.tail = TRUE, log.p = FALSE) qalap(p, location = 0, scale = 1, tau = 0.5, kappa = sqrt(tau/(1-tau)), lower.tail = TRUE, log.p = FALSE) 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 |
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 |
the asymmetry parameter kappa. Must consist of positive values. |
log |
if |
lower.tail, 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 and Kai Huang
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, orange 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 = "orange") abline(h = 0, lty = 2) ## End(Not run) pp <- seq(0.05, 0.95, by = 0.05) # Test two functions max(abs(palap(qalap(pp, loc, sigma, kappa = kappa), loc, sigma, kappa = kappa) - pp)) # Should be 0