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

Authors : Seung Ji NAM, Seong KİM, Hon Keung Tony NG

Pages : 834-856

Doi:10.15672/hujms.959817

View : 26 | Download : 7

Publication Date : 2022-06-01

Article Type : Research Paper

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