Journal of Statistical Theory and Applications

Volume 12, Issue 1, May 2013, Pages 39 - 54

A New Lifetime Model: The Gamma Extended Fréchet Distribution

Authors
Ronaldo V. da Silva, Thiago A.N. de Andrade, Diego B.M. Maciel, Renilma P. S. Campos, Gauss M. Cordeiro
Corresponding Author
Ronaldo V. da Silva
Available Online 1 May 2013.
DOI
https://doi.org/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.
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This is an open access article distributed under the CC BY-NC license.

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Journal
Journal of Statistical Theory and Applications
Volume-Issue
12 - 1
Pages
39 - 54
Publication Date
2013/05
ISSN (Online)
2214-1766
ISSN (Print)
1538-7887
DOI
https://doi.org/10.2991/jsta.2013.12.1.4How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

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
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  - https://doi.org/10.2991/jsta.2013.12.1.4
ID  - Silva2013
ER  -