An Improved Version of Exponential Rayleigh Distribution with Statistical Properties and Diverse Applications

Numerous classical probability distributions have shown little adaptability in recent decades when successfully representing the complexity of real-world data sets, including complex, symmetric, asymmetric, and skewed data sets. This has encouraged researchers to add more parameters to traditional models to create more flexible families of distributions. In this study, we introduced a novel extension of the exponential Rayleigh distribution utilizing a weighted general class of distributions (WG-ERD). The cumulative distribution function (CDF) and probability distribution function (PDF) of the proposed WG-ERD are given respectively as

G(w)=log(1+(1-exp(-aw²-cw))^b)/log(2),

and

g(w)=b(2aw+c)exp(-aw²-cw)(1-exp(-aw²-cw))^b-1/log(2)(1+(1-exp(-aw²-cw))^b).

About its density and hazard functions, the suggested model is highly adaptable and provides a variety of behaviors. The statistical and reliability properties of the proposed distribution are thoroughly established, including the quantile function, moments, skewness, kurtosis, and order statistics. Parameter estimation employs both Bayesian and classical methods, including maximum likelihood, maximum product spacing, and Bayes estimators based on various loss functions. A simulation experiment illustrating the efficacy of the suggested distribution reveals that the Bayes estimator based on the square error loss function generates more precise parameter estimates than other approaches. Finally, two data sets are analyzed to investigate the new distribution's advantage and adaptability. When the suggested model is applied to the various probability distributions currently in use, we find that it provides the best fit compared to competing distributions based on specific evaluation criteria.