Document Type : Research Manuscript

Authors

• zahra Karimiezmareh ¹
• Behdad Mostafaiy ²

¹ Department of Statistics, Allameh Tabataba’i University, Tehran, Iran

² Department of Statistics, University of Mohaghegh Ardabili, Ardabil, Iran

Abstract

In this paper, we propose a new two-parameter discrete distribution based on central Bell expansion, which is zero-inflated and designed to effectively model overdispersed count data. We study several structural properties of the proposed distribution and demonstrate that it is infinitely divisible, which adds theoretical strength and potential for wider applicability. The paper also discusses parameter estimation techniques for the distribution, focusing on two common approaches: the method of moments and the maximum likelihood estimation method. Both methods are developed and explained in detail. To evaluate the accuracy and reliability of these estimators, a simulation study is conducted across different sample sizes, allowing us to assess their performance under various conditions. To illustrate the practical importance and usefulness of the new distribution, we apply it to two real data sets and show how well it fits the observed data, reinforcing its value as a flexible tool for analyzing count data.

Keywords

• Central Bell distribution
• Count data
• Overdispersion
• Zero-inflated

Main Subjects

• Computational Statistics