A Novel Class of Extreme Value Distributions Derived from the KM Transformation of the Generalized Extreme Value Distribution

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DOI: https://doi.org/10.28924/2291-8639-23-2025-274
Published: Nov 5, 2025
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P. Khamrot, N. Deetae, A Novel Class of Extreme Value Distributions Derived from the KM Transformation of the Generalized Extreme Value Distribution, Int. J. Anal. Appl., 23 (2025), 274.

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P. Khamrot, N. Deetae

Abstract

Modeling extreme events is crucial in various disciplines such as environmental sciences, hydrology, finance, and engineering. This paper introduces the KM-transformed Generalized Extreme Value (KMGEV) distribution, a novel and flexible model that generalizes the classical Generalized Extreme Value (GEV) distribution using the KM transformation framework recently proposed by Kavya and Manoharan. We derive the key statistical properties of the KMGEV distribution, including the probability density function (PDF), cumulative distribution function (CDF), survival function, hazard rate function, and quantile function. Additionally, we explore order statistics and their expected values. Parameter estimation is carried out via Maximum Likelihood Estimation (MLE) methods. Through Monte Carlo simulations, we investigate the impact of the shape parameter on moments such as skewness and kurtosis. Graphical analysis highlights the flexibility of the KMGEV model, suggesting its potential in modeling a variety of extreme value phenomena.

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