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http://dx.doi.org/10.5351/CSAM.2017.24.4.397

A new extended Birnbaum-Saunders model with cure fraction: classical and Bayesian approach  

Ortega, Edwin M.M. (Departamento de Ciencias Exatas, Universidade de Sao Paulo)
Cordeiro, Gauss M. (Departamento de Estatistica, Universidade Federal de Pernambuco)
Suzuki, Adriano K. (Departamento de Matematica Aplicada e Estatistica, Universidade de Sao Paulo)
Ramires, Thiago G. (Departamento de Ciencias Exatas, Universidade de Sao Paulo)
Publication Information
Communications for Statistical Applications and Methods / v.24, no.4, 2017 , pp. 397-419 More about this Journal
Abstract
A four-parameter extended fatigue lifetime model called the odd Birnbaum-Saunders geometric distribution is proposed. This model extends the odd Birnbaum-Saunders and Birnbaum-Saunders distributions. We derive some properties of the new distribution that include expressions for the ordinary moments and generating and quantile functions. The method of maximum likelihood and a Bayesian approach are adopted to estimate the model parameters; in addition, various simulations are performed for different parameter settings and sample sizes. We propose two new models with a cure rate called the odd Birnbaum-Saunders mixture and odd Birnbaum-Saunders geometric models by assuming that the number of competing causes for the event of interest has a geometric distribution. The applicability of the new models are illustrated by means of ethylene data and melanoma data with cure fraction.
Keywords
Bayesian estimation; Birnbaum-Saunders distribution; lifetime data distribution; maximum likelihood estimation; simulations;
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