On q-Generalized Extreme Values under Power Normalization with Properties, Estimation Methods and Applications to COVID-19 Data

This paper introduces the q-analogues of the generalized extreme value distribution and its discrete counterpart under power normalization. The inclusion of the parameter q enhances modeling flexibility. The continuous extended model can produce various types of hazard rate functions, with supports that can be finite, infinite, or bounded above or below. Additionally, these new models can effectively handle skewed data, particularly those with highly extreme observations. Statistical properties of the proposed continuous distribution are presented, and the model parameters are estimated using various approaches. A simulation study evaluates the performance of the estimators across different sample sizes. Finally, three distinct real datasets are analyzed to demonstrate the versatility of the proposed model.