Unified framework, statistical properties and estimation of cubic transmuted Rayleigh distributions

Geraldo, Issa Cherif; Katchekpele, Edoh; Kpanzou, Tchilabalo Abozou

doi:10.22080/cjms.2025.29500.1764

Unified framework, statistical properties and estimation of cubic transmuted Rayleigh distributions

Document Type : Research Articles

Authors

¹ Department of Mathematics, Faculty of Sciences, Université de Lomé

² Department of Mathematics, Faculté des Sciences et Techniques, Université de Kara

10.22080/cjms.2025.29500.1764

Abstract

Transmutation is a widely used technique to enhance the flexibility of baseline probability distributions in statistical modelling. While the quadratic transmutation is unique, the cubic transmutation admits multiple formulations. This paper presents a unified investigation of cubic transmuted Rayleigh distributions from both theoretical and empirical perspectives. On the theoretical side, we revisit six existing cubic transmutation formulas and their modified versions, and we introduce a general formulation that encompasses these models while establishing their main statistical properties. To evaluate parameter estimation, simulation studies are conducted to assess the efficiency of maximum likelihood estimators, evaluating performance across different sample sizes and parameter settings, showing satisfactory performance across different scenarios. On the empirical side, real data analyses highlight the comparative performance of the proposed models, with some formulations providing improved fit and flexibility. Overall, this study offers a comprehensive framework that consolidates existing approaches, extends the family of cubic transmuted Rayleigh distributions, and provides practical guidance for their application in data analysis.

Keywords