Inference procedures for the Birnbaum–Saunders distribution and its generalizations

Goodness-of-fit tests are constructed for the two-parameter Birnbaum–Saunders distribution in the case where the parameters are unknown and are therefore estimated from the data. With each test the procedure starts by computing efficient estimators of the parameters. Then the data are transformed to normality and normality tests are applied on the transformed data, thereby avoiding reliance on parametric asymptotic critical values or the need for bootstrap computations. Two classes of tests are considered, the first class being the classical tests based on the empirical distribution function, while the other class utilizes the empirical characteristic function. All methods are extended to cover the case of generalized three-parameter Birnbaum–Saunders distributions.