A New Lifetime Model: The Gamma Extended Fréchet Distribution

DOI

10.2991/jsta.2013.12.1.4How to use a DOI?

Keywords

Fréchet distribution; gamma extended Fr´echet distribution; maximum likelihood; observed information matrix; Weibull distribution.Keywords: Extreme values theory; Asymptotic distribution; Functional Gaussian and nongaussian laws; Uniform entropy numbers; Asymptotic tightness, Stochastic process of

Abstract

For the first time, a four-parameter lifetime model, called the gamma extended Fr´echet distribution, is defined and studied. We obtain some of its mathematical properties. Explicit expressions for the ordinary and incomplete moments, quantile function, mean deviations, R´enyi entropy and reliability are provided. The order statistics and their moments are derived. The method of maximum likelihood is used for estimating the model parameters.We determine the observed information matrix. An application to a real data set shows that the new distribution can provide a better fit than other classical lifetime models. We hope that this generalization may attract wider applications in reliability, biology and survival analysis.

Copyright

© 2013, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Ronaldo V. da Silva
AU  - Thiago A.N. de Andrade
AU  - Diego B.M. Maciel
AU  - Renilma P. S. Campos
AU  - Gauss M. Cordeiro
PY  - 2013
DA  - 2013/05/01
TI  - A New Lifetime Model: The Gamma Extended Fréchet Distribution
JO  - Journal of Statistical Theory and Applications
SP  - 39
EP  - 54
VL  - 12
IS  - 1
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.2013.12.1.4
DO  - 10.2991/jsta.2013.12.1.4
ID  - Silva2013
ER  -