paep {AEP}R Documentation

Computing the cumulative distribution function (cdf) of asymmetric exponential power (AEP) distribution.

Description

Computes the cdf of AEP distribution that is given by

F_{X}(x|Θ)=≤ft\{\begin{array}{*{20}c} \frac{1-ε}{2}-\frac{1-ε}{2 Γ\bigl(1+\frac{1}{α}\bigr)} γ\Bigl(\Big|\frac{μ-x}{σ(1-ε)}\Big|^{α},\frac{1}{α}\Bigr),~{}~x ≤q μ,\\ \frac{1-ε}{2}+\frac{1+ε}{2 Γ\bigl(1+\frac{1}{α}\bigr)} γ\Bigl(\Big|\frac{x-μ}{σ(1+ε)}\Big|^{α},\frac{1}{α}\Bigr),~{{}}~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,ν) =\int_{0}^{u}t^{ν-1}\exp\bigl\{-t\bigr\}dt.

for ν>0.

Usage

paep(x, alpha, sigma, mu, epsilon, log.p = FALSE, lower.tail = TRUE)

Arguments

x

Vector of observations.

alpha

Tail thickness parameter.

sigma

Scale parameter.

mu

Location parameter.

epsilon

Skewness parameter.

log.p

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

lower.tail

If FALSE, then 1-F_{X}(x|Θ) is returned.

Value

Computed cdf of AEP distribution at points of vector x.

Author(s)

Mahdi Teimouri

Examples

paep(x = 2, alpha = 1.5, sigma = 1, mu = 0, epsilon = 0.5, log.p = FALSE, lower.tail = TRUE)

[Package AEP version 0.1.2 Index]