Advances in Pure Mathematics, 2023, 13, 425-441 https://www.scirp.org/journal/apm ISSN Online: 2160-0384 ISSN Print: 2160-0368 DOI: 10.4236/apm.2023.137027 Jul. 12, 2023 425 Advances in Pure Mathematics Estimating the Components of a Mixture of Extremal Distributions under Strong Dependence Carolina Crisci , Gonzalo Perera , Lia Sampognaro Departamento Modelización Estadística de Datos e Inteligenica Artificial (MEDIA), CURE, Rocha, Universidad de la República, Rocha, Uruguay Abstract In this paper, we provide a method based on quantiles to estimate the para- meters of a finite mixture of Fréchet distributions, for a large sample of strongly dependent data. This is a situation that appears when dealing with environmental data and there was a real need of such method. We validate our approach by means of estimation and goodness-of-fit testing over simu- lated data, showing an accurate performance. Keywords Mixture of Extremal Distributions, Strongly Dependent Data 1. Introduction In many applications of Statistics, the finite mixture model had been widely used to describe the distribution of data. A finite mixture model is a distribution that may be written as a finite, convex linear combination of distributions belonging to parametric classes. For instance, a mixture of k normal distributions, each one with its mean and variance, is a basic example, where the parameters involved are 1 − k non-negative weights (because their sum is one), and the 2k parame- ters corresponding to each mean and variance, making a total of 3 1 − k para- meters. In both theoretical developments and specific applications, the use of fi- nite mixture models and the development of techniques of estimation of the unknown parameters have been deeply studied, with developments such as the expectation-maximization algorithm (EM) and its variants [1] [2] [3] [4] [5]. It should be noticed that the parametric classes of distributions involved in the mixture may be different. For instance, one may consider a mixture of a Normal How to cite this paper: Crisci, C., Perera, G. and Sampognaro, L. (2023) Estimating the Components of a Mixture of Extremal Distributions under Strong Dependence. Advances in Pure Mathematics, 13, 425-441. https://doi.org/10.4236/apm.2023.137027 Received: June 1, 2023 Accepted: July 9, 2023 Published: July 12, 2023 Copyright © 2023 by author(s) and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Open Access