The palaplace returns the Cumulative Distribution Function at point x
for the Asymmetric Laplace distribution with parameters \(a*\) and \(m\).
palaplace(x, m = 0, al = 1, ar = 1)a vector containing the values for the probabilities.
(numeric) - value in the range \((-\infty, \infty)\) to evaluate the density.
(numeric) - location parameter.
(numeric) - scale parameters. Must be in the range \((0, \infty)\).
The Asymmetric Laplace distribution is a distribution controlled by three parameters, with formula: $$f(x;a_l,a_r,m) = \frac{1}{A} e^{-|\frac{x-m}{a_l}| }, x < m $$ $$f(x;a_l,a_r,m) = \frac{1}{A} e^{-|\frac{x-m}{a_r}| }, x > m $$ with: $$A = a_l + a_r$$ where \(a*\) are scale parameters, and \(m\) is a location parameter. It is basically derived from the Asymmetric Exponential Power distribution by setting \(b_l = b_r = b\).