Estimation and statistical properties of the Weibull–Rayleigh model with applications to industrial data

Modeling and fitting more complex data sets is an important domain in applied sciences, especially in survival, industry, finance, insurance, and engineering analysis. In this paper, the novel Weibull–Rayleigh distribution was developed using a Weibull-G technique. This new modification improves flexibility for analyzing skewed, symmetry, and heavy-tailed data. The proposed model can be applied in several domains: environment, insurance, industry, and biology. The density function of this newly defined distribution exhibits characteristics of symmetric, asymmetric, complex, and skewed shapes. Several statistical attributes of the proposed model were obtained. These characteristics include a quantile function, ordinary moments, order statistics, entropy measures, and moment-generating functions. Different classical estimation techniques are used to estimate the model parameters of the proposed distribution, and detailed simulation experiments identified the most effective approach. Two data sets from the industry field were applied to demonstrate the practicality and efficiency of the new model, where it was found to provide superior results compared to other competing distributions.