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The Zero-inflated Negative Binomial-Exponential Distribution and Its Application

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Abstract

A new distribution, the zero-inflated negative binomial-exponential (ZINB-E) distribution, is proposed. It is a mixture of a point mass at zero and a negative binomial-exponential (NB-E) distribution. The ZINB-E is an alternative distribution for count data with extra zeros and over-dispersion. We apply the method of maximum likelihood estimation for estimating parameters of the proposed distribution, and derive some of its mathematical properties. We also apply the proposed distribution to fit real data sets that have an excess of zero-count data. The result shows that the ZINB-E distribution is the best model for fitting data compared to the zero-inflated Poisson and zero-inflated negative binomial distributions.

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ACKNOWLEDGMENTS

The first author would like to thank the College of Industrial Technology, King Mongkut’s University of Technology North Bangkok (KMUTNB) for financial support of this research.

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Authors and Affiliations

  1. College of Industrial Technology, King Mongkut’s University of Technology North Bangkok, 10800, Bangkok, Thailand

    Rujira Bodhisuwan

  2. Department of Mathematics and Statistics, University of Regina, S4S 0A2, Regina, Saskatchewan, Canada

    Adam Kehler

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  1. Rujira Bodhisuwan
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  2. Adam Kehler
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Correspondence to Rujira Bodhisuwan or Adam Kehler.

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(Submitted by A. I. Volodin)

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Bodhisuwan, R., Kehler, A. The Zero-inflated Negative Binomial-Exponential Distribution and Its Application. Lobachevskii J Math 42, 300–307 (2021). https://doi.org/10.1134/S1995080221020062

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  • DOI: https://doi.org/10.1134/S1995080221020062

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