The Odd Generalized Rayleigh Reciprocal Weibull Family of Distributions with Applications

Abstract

We introduced a novel family of models in this paper, which we named the odd-generalized Rayleigh reciprocal Weibull-G (OGR-RW-G) family. This family is noteworthy because it applies the T-X model construction technique to the generalized Rayleigh reciprocal Weibull model, addressing the inflexibility limits associated with traditional models and allowing one to use any baseline distribution. We examine some valuable statistical inferences from the OGR-RW-G, including its probability density function (pdf) represented in a linear fashion, its order statistics' pdf, moments, residual life functions and R\'enyi entropy. Additionally, the hazard rate functions (hrfs) and pdfs of a few particular models are determined to have analytical shapes. The OGR-RW-G model parameters are determined by the widely recognized maximum likelihood estimation (MLE) technique. We also perform a simulation exercise to evaluate the performance of the MLEs. Ultimately, the utility of the OGR-RW-G family is demonstrated by using the odd generalized Rayleigh reciprocal Weibull Burr-XII (OGR-RW-BXII) example of the OGR-RW-G to two distinct datasets. In actuality, the four parameter OGR-RW-BXII outperforms the four parameter non-nested models and some nested models that are presented.