fitaep {AEP}R Documentation

Estimating the parameters of AEP distribution through the expectation-maximization (EM) algorithm

Description

Estimates the parameters of AEP distribution for which the pdf 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<∞, and -1<ε<1.

Usage

fitaep(x, initial = FALSE, starts)

Arguments

x

Vector of observations.

initial

By default is FALSE. If the initial values are given by user, then set initial=TRUE.

starts

If initial values are not given by user, i.e., initial=FALSE, then vector starts must contain the initial values of the parameter vector, i.e., starts=\bigl(α^{(0)}, σ^{(0)}, μ^{(0)}, ε^{(0)} \bigr) for starting the EM algorithm.

Value

A list of objects in two parts as

  1. The EM estimator for the parameters of AEP distribution.

  2. A sequence of goodness-of-fit measures consist of Akaike Information Criterion (AIC), Consistent Akaike Information Criterion (CAIC), Bayesian Information Criterion (BIC), Hannan-Quinn information criterion (HQIC), Anderson-Darling (AD), Cram\'eer-von Misses (CVM), Kolmogorov-Smirnov (KS), and log-likelihood (log-likelihood) statistics.

Author(s)

Mahdi Teimouri

References

A. P. Dempster, N. M. Laird, and D. B. Rubin, 1977. Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society Series B, 39, 1-38.

Examples

x <- raep(n=50, alpha=.8, sigma=1, mu=0, epsilon=0.5)
fitaep(x, initial = FALSE, starts)

[Package AEP version 0.1.2 Index]