Theoretical results and modeling under the discrete Birnbaum-Saunders distribution

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.

Keywords:

• Birnbaum-Saunders distribution
• maximum likelihood
• Monte Carlo simulation
• R software
• regression model

Acknowledgments

The authors express their sincere thanks to the Associate Editor and the anonymous reviewer for their useful comments and suggestions on an earlier version of this manuscript which led to this much improved version.

Notes

1 Sen et al. (2010) derived the discrete BS but the authors did not present specific properties of the distribution. They presented only the probability mass function, survival function, hazard rate, reverse hazard rate, and maximum likelihood estimators. A brief application to real data was also presented.

Additional information

Funding

Helton Saulo gratefully acknowledges financial support from CNPq and FAP-DF. Jeremias Leão gratefully acknowledges financial support from CNPq and FAPEAM-AM. Filidor Vilca gratefully acknowledges financial support from FAPESP (grant number 2020/16713-0).