Discrete Burr-Hatke Distribution With Properties, Estimation Methods and Regression Model

M El-Morshedy,Emrah Altun,M S Eliwa

doi:10.1109/access.2020.2988431

Abstract

A new one-parameter discrete distribution, namely discrete Burr-Hatke distribution is introduced and its mathematical properties are studied comprehensively. The main properties of the discrete Burr-Hatke distribution such as mean, variance, skewness and kurtosis measures are obtained in explicit forms. Several parameter estimation methods are used to obtain unknown model parameters and these estimation methods are compared via simulation study. The discrete Burr-Hatke distribution is over-dispersed since its variance is greater than its mean. This property of the proposed distribution opens a new opportunity to model over-dispersed data sets. To show the importance of the proposed distribution against the existing discrete probability distributions, three data sets in different fields are analyzed. Additionally, count regression model based on the discrete Burr-Hatke distribution is introduced with its residual analysis.

Highlights

Modeling the number of occurrences of events is an important issue and gains much attention in recent years
This study introduces a flexible discrete distribution to model these kind of data sets
The main advantage of the discrete Burr-Hatke (DBH) distribution against the existing ones is that the statistical properties of the DBH distribution are in explicit forms which are important in statistical inference

Summary

Introduction

Modeling the number of occurrences of events is an important issue and gains much attention in recent years. These types of data sets are modeled by discrete probability distributions such as Poisson, negative-binomail, geometric, Poisson-Lindley etc. The main goal of these studies is to provide an alternative model in modeling the over-dispersed or under-dispersed count data sets. These distributions are obtained by using the survival discretization method. Let the random variable X has the survival function such as S(x) = Pr(X > x). The probability mass function (pmf) of the discrete random variable X is

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Conclusion