Theoretical results and modeling under the discrete Birnbaum-Saunders distribution

TL;DR

This paper explores the properties of a discrete Birnbaum-Saunders distribution, proves its unimodality, and introduces a regression model with parameter estimation evaluated through simulations and real data applications.

Contribution

It provides the first theoretical analysis of the discrete Birnbaum-Saunders distribution and proposes a new regression model based on it.

Findings

Proved unimodality of the distribution

Developed maximum likelihood estimators for model parameters

Validated the model with real data examples

Abstract

In this paper, we discuss some theoretical results and properties of a discrete version of the Birnbaum-Saunders distribution. We present a proof of the unimodality of this model. Moreover, results on moments, quantile function, reliability and order statistics are also presented. In addition, we propose a regression model based on the discrete Birnbaum-Saunders distribution. The model parameters are estimated by the maximum likelihood method and a Monte Carlo study is performed to evaluate the performance of the estimators. Finally, we illustrate the proposed methodology with the use of real data sets.