J Indian Soc Probab Stat https://doi.org/10.1007/s41096-018-0044-1 RESEARCH ARTICLE Statistical Inference for Type-I Generalized Birnbaum–Saunders Distribution Ronghua Wang 1 · Naijun Sha 2 · Xiaoling Xu 3 Accepted: 11 May 2018 © The Indian Society for Probability and Statistics (ISPS) 2018 Abstract A new generalized Birnbaum–Saunders distribution (Type-I GBS) was pre- sented 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 tradi- tional maximum likelihood estimation approach, and propose a new inference method for the GBS-I distribution. An extensive simulation study is carried out to assess per- formance 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. Keywords Birnbaum–Saunders distribution · Generalization · Likelihood · Estimation · Hypothesis test B Naijun Sha nsha@utep.edu Ronghua Wang wrhxxl@shnu.edu.cn Xiaoling Xu xlxu@suibe.edu.cn 1 College of Mathematics and Science, Shanghai Normal University, 200234 Shanghai, China 2 Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, USA 3 Shanghai University of International Business and Economics, 201600 Shanghai, China 123