Bayesian and frequentist approaches on estimation and testing for a zero-inflated binomial distribution

Abstract

To analyze discrete count data with excessive zeros, different zero-inflated statistical models that allow for frequent zero-valued observations have been developed. When the underlying data generation process of non-zero values is based on the number of successes in a sequence of independent Bernoulli trials, the zero-inflated binomial distribution is perhaps adequate for modeling purposes. In this paper, we discuss statistical inference for a zero-inflated binomial distribution using the objective Bayesian and frequentist approaches. Point and interval estimation of the model parameters and hypothesis testing for excessive zeros in a zero-inflated binomial distribution are developed. A Monte Carlo simulation study is used to assess the performance of estimation and hypothesis testing procedures. A comparative study of the objective Bayesian approach and the frequentist approach is provided. The proposed statistical inferential methods are applied to analyze an earthquake dataset and a baseball dataset for illustration.

Keywords

• Bayes factor
• binomial distribution
• EM algorithm
• Jeffreys prior
• maximum likelihood estimate
• zero-inflated models

Supporting Institution

National Research Foundation of Korea

Project Number

NRF-2021R1A2C1005271

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