Advances and Applications in Statistics

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ON THE ZERO AND k-INFLATED NEGATIVE BINOMIAL DISTRIBUTION WITH APPLICATIONS

Authors

  • Ian Jay A. Serra
  • Daisy Lou L. Polestico

Keywords:

inflated count data, overdispersion, ZkINB distribution, excessive counts, negative binomial distribution, count distributions

DOI:

https://doi.org/10.17654/0972361723037

Abstract

In the literature, there are a significant number of studies on mixtures and compound probability distributions used for count data with inflated frequencies. This study extended some existing zero-inflated distributions, by considering the flexibility of peaks in the data with excessive counts other than zeros and handled an overdispersion in the data. Moreover, this study formulated a proposed zero- and k-inflated negative binomial (ZkINB) distribution which is a mixture of a multinomial logistic and negative binomial distribution. The multinomial logistic component captures the occurrence of excessive counts, at zero and at k > 0, while the negative binomial component captures the counts that are assumed to follow a negative binomial distribution. The probability mass function (pmf) and the moment generating function (mgf ) of the distribution were derived in order to compute some vital structural properties of the formulated distribution, such as the mean and the variance. Examples showed  that the formulated ZkINB seems to capture better distributions as compared with other existing distributions for inflated count data.

Received: August 30, 2022 
Revised: March 3, 2023 
Accepted: May 18, 2023 

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Published

24-09-2025

Issue

Vol. 88 No. 1 (2023)

Section

Articles

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How to Cite

ON THE ZERO AND k-INFLATED NEGATIVE BINOMIAL DISTRIBUTION WITH APPLICATIONS. (2025). Advances and Applications in Statistics , 88(1), 1-23. https://doi.org/10.17654/0972361723037

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