Multiple Parameter Generalized Rayleigh distribution with Application to Real Dataset

Abstract

This work presents the Multi-Parameter Generalized Rayleigh (MPGR) Distribution, a new probability distribution that adds a scale parameter to the traditional Generalized Rayleigh distribution. This extension aims to enhance the flexibility and applicability of the Rayleigh distribution in various statistical modeling scenarios.  The inclusion of the additional scale parameter allows the MPGR to accommodate a broader range of data distributions and capture more complex underlying patterns. A few of the model's statistical characteristics are examined. The model's parameters are estimated via maximum likelihood estimation. We have applied the MPGR to a real dataset, demonstrating its capability to provide a superior fit compared to traditional distributions. Sensitivity analysis showed that parameters alpha, beta, and lambda significantly influence the model's shape and behavior. Through empirical analysis, we have showed that the MPGR offers improved modeling accuracy and flexibility, making it a valuable tool for statistical inference and data analysis. Our results highlight the practical benefits of this new distribution in various applications, from reliability engineering to financial modeling, thus contributing to the advancement of statistical methodologies. All the graphical and analytical calculations are performed using R programming language.