daep {AEP}R Documentation

Computing the probability density function (pdf) of asymmetric exponential power (AEP) distribution.

Description

Computes the pdf of AEP distribution that is given by

f_{X}(x|Θ)=≤ft\{\begin{array}{*{20}c} \frac{1}{2σ Γ\bigl(1+\frac{1}{α}\bigr)}\exp\biggl\{-\bigg|\frac{μ-x}{σ(1-ε)}\bigg|^{α}\biggr\},~~{}~x ≤q μ,\\ \frac{1}{2σ Γ\bigl(1+\frac{1}{α}\bigr)}\exp\biggl\{-\bigg|\frac{x-μ}{σ(1+ε)}\bigg|^{α}\biggr\},~~{}~x>μ, \end{array} \right.

where -∞<x<+∞, Θ=(α,σ,μ,ε)^T with 0<α ≤q 2, σ> 0, -∞<μ<∞, -1<ε<1, and

Γ(u)=\int_{0}^{+∞} x^{u-1}\exp\bigl\{-x\bigr\}dx,

for u>0.

Usage

daep(x, alpha, sigma, mu, epsilon, log = FALSE)

Arguments

x

Vector of observation of requested random realizations.

alpha

Tail thickness parameter.

sigma

Scale parameter.

mu

Location parameter.

epsilon

Skewness parameter.

log

If TRUE, then log\bigl(f_{X}(x|Θ)\bigr) is returned.

Details

Note that if ε=0, then the AEP distribution turns into a normal distribution with mean μ and standard deviation √{2}σ. When α=2, the AEP distribution is a slight variant of that of

Value

Computed pdf of AEP distribution at points of vector x.

Author(s)

Mahdi Teimouri

References

G. S. Mudholkar and A. D. Huston, 2001. The epsilon-skew–normal distribution for analyzing near-normal data.Journal of Statistical Planning and Inference, 83, 291-309.

Examples

daep(x = 2, alpha = 1.5, sigma = 1, mu = 0, epsilon = 0.5, log = FALSE)

[Package AEP version 0.1.2 Index]