A new distribution with decreasing, increasing and upside-down bathtub failure rate

Authors:
Rodrigo B. Silva;Wagner Barreto-Souza;Gauss M. Cordeiro
Affiliations:
Universidade Federal de Pernambuco, Departamento de Engenharia de Produção, Brazil;Universidade Federal de Pernambuco, Departamento de Estatística, Cidade Universitária, 50740-540-Recife, PE, Brazil;Universidade Federal Rural de Pernambuco, Departamento de Estatística e Informática, Brazil
Venue:
Computational Statistics & Data Analysis
Year:
2010

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Abstract

The modeling and analysis of lifetimes is an important aspect of statistical work in a wide variety of scientific and technological fields. For the first time, the so-called generalized exponential geometric distribution is introduced. The new distribution can have a decreasing, increasing and upside-down bathtub failure rate function depending on its parameters. It includes the exponential geometric (Adamidis and Loukas, 1998), the generalized exponential (Gupta and Kundu, 1999) and the extended exponential geometric (Adamidis et al., 2005) distributions as special sub-models. We provide a comprehensive mathematical treatment of the distribution and derive expressions for the moment generating function, characteristic function and rth moment. An expression for Renyi entropy is obtained, and estimation of the stress-strength parameter is discussed. We estimate the parameters by maximum likelihood and obtain the Fisher information matrix. The flexibility of the new model is illustrated in an application to a real data set.