dal {lqmix} | R Documentation |
Compute the density for the three parameter Asymmetric Laplace Distribution
dal(y, mu = 0, sigma = 1, qtl = 0.5, log = FALSE)
y |
vector of quantiles |
mu |
location parameter |
sigma |
scale parameter |
qtl |
skewness parameter |
log |
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}))
Return the density for the asymmetric Laplace distribution
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.