dal {lqmix}

Density of the Asymmetric Laplace distribution

Description

Compute the density for the three parameter Asymmetric Laplace Distribution

Usage

dal(y, mu = 0, sigma = 1, qtl = 0.5, log = FALSE)

Arguments

y

vector of quantiles

mu

location parameter

sigma

scale parameter

qtl

skewness parameter

log

logical; if TRUE, probabilities are log-transformed

Details

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}))

Value

Return the density for the asymmetric Laplace distribution

References

Koenker R, Machado JAF (1999). “Goodness of fit and related inference processes for quantile regression.” Journal of the american statistical association, 94, 1296–1310.

Yu K, Moyeed RA (2001). “Bayesian quantile regression.” Statistics & Probability Letters, 54, 437–447.