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A new extended Birnbaum-Saunders model with cure fraction: classical and Bayesian approach
Ortega, Edwin M.M.,Cordeiro, Gauss M.,Suzuki, Adriano K.,Ramires, Thiago G. The Korean Statistical Society 2017 Communications for statistical applications and me Vol.24 No.4
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.