A new class of fatigue life distributions

TL;DR

This paper introduces a new class of fatigue life distributions by combining Birnbaum-Saunders and power series distributions, providing mathematical properties, special cases, and real data applications.

Contribution

It proposes the Birnbaum-Saunders power series class, a novel distribution family with flexible hazard functions and practical estimation methods.

Findings

The new class includes the two-parameter Birnbaum-Saunders distribution as a special case.

Mathematical properties such as moments and order statistics are derived.

Applications to real data demonstrate the usefulness of the new distributions.

Abstract

In this paper, we introduce the Birnbaum-Saunders power series class of distributions which is obtained by compounding Birnbaum-Saunders and power series distributions. The new class of distributions has as a particular case the two-parameter Birnbaum-Saunders 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.