A new class of fatigue life distributions

Abstract

AbstractIn this paper, we introduce the Birnbaum–Saunders () power series class of distributions which is obtained by compounding and power series distributions. The new class of distributions has as a particular case the two-parameter distribution. The hazard rate function of the proposed class can be increasing and upside-down bathtub shaped. We provide important mathematical properties such as moments, order statistics, estimation of the parameters and inference for large sample. Three special cases of the new class are investigated with some details. We illustrate the usefulness of the new distributions by means of two applications to real data sets.Keywords: Birnbaum–Saunders distributionmaximum likelihood estimationorder statisticpower series distributionAMS Subject Classifications: 62E1062E1562E99 AcknowledgementsThe financial support from the Brazilian governmental institutions CNPq and CAPES is gratefully acknowledged.