A class of generalized Birnbaum‐Saunders distributions for reliability modeling

Abstract

In this paper, we generalize the Birnbaum‐Saunders (BS) distribution by two ways. One is based on the mixture representation of BS distribution, and a flexible weight is adopted to describe the kurtosis of the distribution. The other way is based on the transformation property of BS distribution, and we incorporate a power parameter in the transformation to describe the skewness of the distribution. Then a four‐parameter BS distribution including skewness and kurtosis parameters is induced by combining the two ways. The properties of these generalized BS distributions are investigated. Then, the expectation maximization (EM) algorithm is proposed to estimate the parameters. Real data analysis is performed to illustrate the superiority of the generalized BS distributions. Finally, some potential generalizations are discussed.