A New Lifetime Model: The Gamma Extended Fréchet Distribution

• Published in: Journal of statistical theory and applications Vol. 12; no. 1; pp. 39 - 54
• Main Authors: da Silva, Ronaldo V., de Andrade, Thiago A. N., Maciel, Diego B. M., Campos, Renilma P. S., Cordeiro, Gauss M.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.05.2013; Springer Nature B.V; Springer
• Subjects: Entropy (Information theory); 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; Mathematical models; Parameters; Reliability; Research Article; Stochastic process of; Fréchet distribution; gamma extended Fréchet distribution; Weibull distribution; observed information matrix; maximum likelihood
• ISSN: 1538-7887; 2214-1766; 1538-7887
• DOI: 10.2991/jsta.2013.12.1.4

For the first time, a four-parameter lifetime model, called the gamma extended Fréchet distribution, is defined and studied. We obtain some of its mathematical properties. Explicit expressions for the ordinary and incomplete moments, quantile function, mean deviations, Rényi 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.