A new extension of the Rayleigh distribution: Methodology, classical, and Bayes estimation, with application to industrial data

In statistical modeling, generating a novel family of distributions is essential to develop new and adaptable models to analyze various data sets. This paper presents a new asymmetric extension of the Rayleigh distribution called the generalized Kumaraswamy Rayleigh model. The proposed distribution can fit symmetric, complex, heavy-tailed, and asymmetric data sets. Several key mathematical and statistical results were investigated, including moments, moment-generating functions, variance, dispersion index, skewness, and kurtosis for the suggested model. In addition, various estimation strategies, including maximum likelihood estimation and Bayes estimation, were used to estimate the model parameters. The Metropolis-Hastings technique was used for Bayesian estimates under the square error loss function. A comprehensive simulation study was used to evaluate the performance of the derived estimators. The model's flexibility was tested on two data sets from the industrial domain, revealing that it offers greater flexibility compared to existing distributions.