aldmix {qbld}

Asymmetric Laplace distribution

Description

Cumulative density, probability distribution function, quantile function and random generation for the asymmetric Laplace distribution with quantile p, location parameter mu and scale parameter sigma.

Usage

raldmix(n, mu, sigma, p)

daldmix(x, mu = 0, sigma = 1, p = 0.5)

paldmix(q, mu = 0, sigma = 1, p = 0.5, lower.tail = TRUE)

qaldmix(prob, mu = 0, sigma = 1, p = 0.5, lower.tail = TRUE)

Arguments

n

: number of observations

mu

: location parameter

sigma

: scale parameter

p, prob

: probability at which to calculate quantile

x, q

: vector of quantiles

lower.tail

: logical; decides b/w P(X<=p) or P(X>p) for p/q

Details

The asymmetric Laplace distribution (ALD), which has the following pdf:

f(x;\mu,\sigma,p) = \frac{p(1-p)}{\sigma} \exp\{-\frac{(x-\mu)}{\sigma}(p-I(x \le \mu))\}

If not specified, p=0.5, mu = 0, sigma = 1.

Value

• raldmix returns a vector of random numbers from AL(mu,sigma,p).

• daldmix returns returns density of AL(mu,sigma,p) at point x.

• paldmix returns CDF prob of AL(mu,sigma,p) at quantile q.

• qaldmix returns inverse CDF quantile of AL(mu,sigma,p) at prob.

References

Keming Yu & Jin Zhang (2005) A Three-Parameter Asymmetric Laplace Distribution and Its Extension, Communications in Statistics - Theory and Methods, 34:9-10, 1867-1879, DOI: 10.1080/03610920500199018

Kobayashi, Genya. (2011). Gibbs Sampling Methods for Bayesian Quantile Regression. J Stat Comput Simul. 81. 1565. 10.1080/00949655.2010.496117.

See Also

rgig for random sampling from GIG distribution

Examples

raldmix(n = 10, mu = 5, sigma = 10, p = 0.5)
daldmix(c(4,5),mu = 0,sigma = 1,p = 0.5)
paldmix(c(1,4),mu = 0,sigma = 1,p = 0.5,lower.tail=TRUE)
qaldmix(0.5,mu = 0,sigma = 1,p = 0.5,lower.tail=TRUE)