A Reparameterized Birnbaum–Saunders Distribution and its Moments, Estimation and Applications

Abstract

The Birnbaum–Saunders (BS) distribution is a model that is receiving considerable attention due to its good properties. We provide some results on moments of a reparameterized version of the BS distribution and a generation method of random numbers from this distribution. In addition, we propose estimation and inference for the mentioned parameterization based on maximum likelihood, moment, modified moment and generalized moment methods. By means of a Monte Carlo simulation study, we evaluate the performance of the proposed estimators. We discuss applications of the reparameterized BS distribution from different scientific fields and analyze two real-world data sets to illustrate our results. The simulated and real data are analyzed by using the R software.

Keywords

• data analysis
• maximum likelihood and moment estimation
• Monte Carlo method
• random number generation
• statistical software