Biparametric zero-modified power series distributions: Bayesian analysis under a reference prior approach

ABSTRACT

This paper presents a Bayesian approach by considering a reference prior for estimating the parameters of biparametric zero-modified power series (ZMPS) distributions. The ZMPS distribution is an extension of the power series (PS) distribution family, allowing it to be adjusted to count data without previous knowledge of frequency of zero observations in the sample (e.g., zero-inflated or zero-deflated datasets). Simulation studies are presented in order to illustrate the performance of the proposed methodology. Applications of the proposed methodology involve the analysis of three real datasets.

KEYWORDS:

• Count data
• power series distributions
• reference prior
• zero-inflated dataset
• zero-deflated dataset.

Acknowledgments

This work was partially supported by the Brazilian institutions FAPESP and CNPq. The authors would like to thank the Editors and Referees for the detailed review on the manuscript and for their thoughtful comments.