A discrete Ramos-Louzada distribution for asymmetric and over-dispersed data with leptokurtic-shaped: Properties and various estimation techniques with inference

Ahmed Sedky Eldeeb; Muhammad Ahsan-ul-Haq; Mohamed S. Eliwa; Ahmed Sedky Eldeeb; Muhammad Ahsan-ul-Haq; Mohamed S. Eliwa

doi:10.3934/math.2022099

AIMS Mathematics

2022, Volume 7, Issue 2: 1726-1741. doi: 10.3934/math.2022099

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Research article

A discrete Ramos-Louzada distribution for asymmetric and over-dispersed data with leptokurtic-shaped: Properties and various estimation techniques with inference

1.
Department of Business Administration, College of Business, King Khalid University, Saudi Arabia
2.
Department of Statistics, Mathematics and Insurance, Alexandria University, Egypt
3.
College of Statistical & Actuarial Sciences, University of the Punjab, Lahore, Pakistan
4.
Quality Enhancement Cell, National College of Arts, Lahore, Pakistan
5.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Received: 20 June 2021 Accepted: 26 October 2021 Published: 02 November 2021
MSC : 60E05, 62E10, 62F10, 62N05, 62P10

In this paper, a flexible probability mass function is proposed for modeling count data, especially, asymmetric, and over-dispersed observations. Some of its distributional properties are investigated. It is found that all its statistical properties can be expressed in explicit forms which makes the proposed model useful in time series and regression analysis. Different estimation approaches including maximum likelihood, moments, least squares, Andersonӳ-Darling, Cramer von-Mises, and maximum product of spacing estimator, are derived to get the best estimator for the real data. The estimation performance of these estimation techniques is assessed via a comprehensive simulation study. The flexibility of the new discrete distribution is assessed using four distinctive real data sets ԣoronavirus-flood peaks-forest fire-Leukemia? Finally, the new probabilistic model can serve as an alternative distribution to other competitive distributions available in the literature for modeling count data.
- discretization technique,
- estimation approaches,
- inference,
- asymmetric data,
- overdispersed data
Citation: Ahmed Sedky Eldeeb, Muhammad Ahsan-ul-Haq, Mohamed S. Eliwa. A discrete Ramos-Louzada distribution for asymmetric and over-dispersed data with leptokurtic-shaped: Properties and various estimation techniques with inference[J]. AIMS Mathematics, 2022, 7(2): 1726-1741. doi: 10.3934/math.2022099

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Abstract

In this paper, a flexible probability mass function is proposed for modeling count data, especially, asymmetric, and over-dispersed observations. Some of its distributional properties are investigated. It is found that all its statistical properties can be expressed in explicit forms which makes the proposed model useful in time series and regression analysis. Different estimation approaches including maximum likelihood, moments, least squares, Andersonӳ-Darling, Cramer von-Mises, and maximum product of spacing estimator, are derived to get the best estimator for the real data. The estimation performance of these estimation techniques is assessed via a comprehensive simulation study. The flexibility of the new discrete distribution is assessed using four distinctive real data sets ԣoronavirus-flood peaks-forest fire-Leukemia? Finally, the new probabilistic model can serve as an alternative distribution to other competitive distributions available in the literature for modeling count data.

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