dal function

The Asymmetric Laplace Distribution

The Asymmetric Laplace Distribution

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)

Arguments

  • x: vector of quantiles (dal, pal) or probabilities (qal).
  • n: number of observations.
  • mu: location parameter.
  • sigma: positive scale parameter.
  • tau: skewness parameter (0,1).
  • log: logical; if TRUE, probabilities are log--transformed.

Details

The asymmetric Laplace distribution with parameters (mu, sigma, tau) has density

f(x)=τ(1τ)/σe1/(2σ)(θmax(x,0)+(1θ)max(x,0)) f(x) = \tau(1-\tau)/\sigma e^{-1/(2\sigma) (\theta max(x,0) + (1 - \theta) max(-x,0))}

Author(s)

Marco Geraci

See Also

lqmm, lqm

  • Maintainer: Marco Geraci
  • License: GPL (>= 2)
  • Last published: 2022-04-06

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