A mixture transmuted generalized extreme value distribution: Definition and properties

¹ The National Key Laboratory of Water Disaster Prevention, Hohai University, Nanjing 210098, Jiangsu, China
² College of Mechanics and Engineering Science, Hohai University, Nanjing 210098, Jiangsu, China
³ School of Architecture and Civil Engineering, HuangShan University, Huangshan 245041, Anhui, China

^* Corresponding author: 114024@hsu.edu.cn

Published online: 9 July 2025

Abstract

Extreme events are often described using generalized extreme value models, which are crucial for quantifying their impact. In prior studies, researchers have utilized the quadratic rank transmutation map to construct a comprehensive family of probability distributions, incorporating an additional parameter to significantly improve the flexibility of distribution modeling. To gain a deeper understanding of the statistical characteristics and patterns of extreme events, mixture distributions have been applied, such as the mixture normal distribution and the mixture of Gumbel distribution, among others. However, the applicability of a single transmuted generalized extreme value distribution is somewhat limited. In many practical scenarios, the available data can be attributed to two or more contributing factors. This concept enables us to combine statistics properties from different distributions to derive new distributions that encapsulate the properties of their components. The development of the mixture transmuted generalized extreme value distribution is motivated by this need and is derived from the transmuted generalized extreme value distribution. In this paper, the properties of the survival function, hazard rate function, mean and variance, and maximum likelihood estimations of the mixture transmuted generalized extreme value distribution are provided, also the corresponding equations are given.