loglapUC {VGAM} | R Documentation |
Density, distribution function, quantile function and random generation
for the 3-parameter log-Laplace distribution with location
parameter location.ald
, scale parameter scale.ald
(on the log scale),
and asymmetry parameter kappa
.
dloglap(x, location.ald = 0, scale.ald = 1, tau = 0.5, kappa = sqrt(tau/(1-tau)), log = FALSE) ploglap(q, location.ald = 0, scale.ald = 1, tau = 0.5, kappa = sqrt(tau/(1-tau)), lower.tail = TRUE, log.p = FALSE) qloglap(p, location.ald = 0, scale.ald = 1, tau = 0.5, kappa = sqrt(tau/(1-tau)), lower.tail = TRUE, log.p = FALSE) rloglap(n, location.ald = 0, scale.ald = 1, tau = 0.5, kappa = sqrt(tau/(1-tau)))
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations.
If |
location.ald, scale.ald |
the location parameter xi and the (positive) scale parameter sigma, on the log scale. |
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 |
A positive random variable Y is said to have a log-Laplace
distribution if \log(Y) has an asymmetric Laplace distribution
(ALD). There are many variants of ALDs and the one used here
is described in alaplace3
.
dloglap
gives the density,
ploglap
gives the distribution function,
qloglap
gives the quantile function, and
rloglap
generates random deviates.
T. W. Yee and Kai Huang
Kozubowski, T. J. and Podgorski, K. (2003) Log-Laplace distributions. International Mathematical Journal, 3, 467–495.
dalap
,
alaplace3
,
loglaplace1
.
loc <- 0; sigma <- exp(0.5); kappa <- 1 x <- seq(-0.2, 5, by = 0.01) ## Not run: plot(x, dloglap(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 = "") abline(h = 0, col = "blue", lty = 2) lines(qloglap(seq(0.05,0.95,by = 0.05), loc, sigma, kappa = kappa), dloglap(qloglap(seq(0.05,0.95,by = 0.05), loc, sigma, kappa = kappa), loc, sigma, kappa = kappa), col = "purple", lty = 3, type = "h") lines(x, ploglap(x, loc, sigma, kappa = kappa), type = "l", col = "red") abline(h = 0, lty = 2) ## End(Not run) ploglap(qloglap(seq(0.05,0.95,by = 0.05), loc, sigma, kappa = kappa), loc, sigma, kappa = kappa)