Density, distribution function, quantile function and random generation for the asymmetric Laplace distribution.
dal(x, mu = 0, sigma = 1, tau = 0.5, log = FALSE)
pal(x, mu = 0, sigma = 1, tau = 0.5)
qal(x, mu = 0, sigma = 1, tau = 0.5)
ral(n, mu = 0, sigma = 1, tau = 0.5)vector of quantiles (dal, pal) or probabilities (qal).
number of observations.
location parameter.
positive scale parameter.
skewness parameter (0,1).
logical; if TRUE, probabilities are log--transformed.
The asymmetric Laplace distribution with parameters (mu, sigma, tau) has density $$f(x) = \tau(1-\tau)/\sigma e^{-1/(2\sigma) (\theta max(x,0) + (1 - \theta) max(-x,0))}$$