daep: Computing the probability density function (pdf) of...

In AEP: Statistical Modelling for Asymmetric Exponential Power Distribution

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

Description

The pdf of AEP distribution given by

f_{X}(x|Θ)= \frac{1}{2σ Γ\bigl(1+\frac{1}{α}\bigr)}\exp\biggl\{-\bigg|\frac{μ-x}{σ(1-ε)}\bigg|^{α}\biggr\},~~{}~x < μ,

f_{X}(x|Θ)= \frac{1}{2σ Γ\bigl(1+\frac{1}{α}\bigr)}\exp\biggl\{-\bigg|\frac{x-μ}{σ(1+ε)}\bigg|^{α}\biggr\},~~{}~x ≥qμ,

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,~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

The AEP distribution is a special case of asymmetric exponential power distribution studied by Dongming and Zinde-Walsh (2009) when p_1=p_2=α. Also, 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 epsilon-skew-normal distribution introduced by Mudholkar and Huston (2001).

Value

Computed pdf of AEP distribution at points of vector x.

Author(s)

Mahdi Teimouri

References

Z. Dongming and V. Zinde-Walsh, 2009. Properties and estimation of asymmetric exponential power distribution, Journal of Econometrics, 148(1), 86-99.

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)

AEP documentation built on Sept. 7, 2022, 5:06 p.m.