Exploring the Fréchet–Power Rayleigh Distribution with Statistical Properties and Medical Data Insights

In this article, we introduce a new form of Power Rayleigh distribution using the Topp–Leone generated family of distributions. The new distribution is called the Fréchet–Power Rayleigh distribution. The different structural properties of the distribution are discussed, including moments, moment-generating function, incomplete moments, order statistics, Rényi entropy, and mean deviations. The estimation of the parameters is performed by using the classical maximum likelihood method. A simulation analysis is carried out to evaluate and compare the effectiveness of estimators in terms of their bias, variance and mean square error. Finally, the distribution performance and application are investigated using real-life data from medical science.