Extension Odd Generalized Rayleigh Inverse Rayleigh Distribution: Structure and Properties

Ali Talib Mohammed; Shihab Ahmed  Abdul Reda; Aytekin  Enver

doi:10.30526/39.2.4303

Authors

Ali Talib Mohammed Department of Mathematics, College of Education for Pure Science (Ibn Al-Haitham), University of Baghdad, Baghdad, Iraq. https://orcid.org/0000-0003-0235-2352
Shihab Ahmed Abdul Reda Department of Mathematics, College of Education for Pure Science (Ibn Al-Haitham), University of Baghdad, Baghdad, Iraq. https://orcid.org/0009-0005-4358-6480
Aytekin Enver Department of Mathematics, Gazi University, Teknikokullar, Ankara, Türkiye https://orcid.org/0000-0001-6013-0323

DOI:

https://doi.org/10.30526/39.2.4303

Keywords:

T-X family, point estimation, Inverse Rayleigh, quantile function

Abstract

The Extension Odd Generalized Rayleigh Inverse Rayleigh (EOGRIR) distribution is a novel statistical model that leverages existing distribution families in a flexible manner. This model enhances the ability of standard distributions to analyze data. It makes it easier and faster to examine and model different types of lifetime and reliability data. The essay thoroughly examines the fundamental mathematical characteristics of the EOGRIR distribution. Some examples include series expansions, moments, the quantile, skewness, Rényi entropy, kurtosis, order statistics, and the moment generating function. These traits help us understand how the proposed distribution works and how its mathematical principles operate. We also examine methods for estimating parameters, with a focus on maximum likelihood estimates (MLE), to ensure that inference and parameter estimates are accurate. The EOGRIR distribution is likely to have a significant impact on statistics, as it offers a more flexible and comprehensive framework that may be superior to the existing ones

Author Biographies

Ali Talib Mohammed, Department of Mathematics, College of Education for Pure Science (Ibn Al-Haitham), University of Baghdad, Baghdad, Iraq.

Assistant Professor, Department of Mathematics, College of Education for Pure Sciences (Ibn Al-Haytham), University of Baghdad
Research interests: Applied mathematics, mathematical statistics, and statistical distributions
Shihab Ahmed Abdul Reda, Department of Mathematics, College of Education for Pure Science (Ibn Al-Haitham), University of Baghdad, Baghdad, Iraq.

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Aytekin Enver, Department of Mathematics, Gazi University, Teknikokullar, Ankara, Türkiye

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