Compute the density for the three parameter Asymmetric Laplace Distribution
dal(y, mu = 0, sigma = 1, qtl = 0.5, log = FALSE)Return the density for the asymmetric Laplace distribution
vector of quantiles
location parameter
scale parameter
skewness parameter
logical; if TRUE, probabilities are log-transformed
The function computes the density of the Asymmetric Laplace distribution, with location \(\mu\), scale \(\sigma > 0\)
and skewness qtl = q in (0,1), as discussed by Koenker and Machado (1999) and Yu and Moyeed (2001), according to the following expression
$$f(y | \mu, \sigma, q) = \frac{q(1-q)}{\sigma} \exp(-\rho_{q} (\frac{y-\mu}{\sigma}))$$
ref:dal1lqmix
ref:dal2lqmix