Statistical Inference for Type-I Generalized Birnbaum–Saunders Distribution

A new generalized Birnbaum–Saunders distribution (Type-I GBS) was presented in Owen (IEEE Trans Reliab 55:475–479, 2006) to model a lifetime of a product under cyclic stresses by using a long memory process on the crack extensions. This highly flexible model includes the original BS distribution as a special case and can be widely applied in fatigue studies. In this article, we present the relevant properties, parameter estimation, and hypothesis testing for the distribution. We explore the traditional maximum likelihood estimation approach, and propose a new inference method for the GBS-I distribution. An extensive simulation study is carried out to assess performance of the methods, and a real data is analyzed where it is shown that the GBS-I model with the proposed method provides an efficient estimation and achieves a better fit than the classic likelihood-based procedure.