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Martín Arevalillo, Jorge

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0000-0003-1944-3699
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Martín Arevalillo
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Jorge
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2023 - 20243
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Autor: Navarro, Jorge ×

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Mostrando 1 - 3 de 3
  • Miniatura
    Publicación
    A New Separation Index and Classification Techniques Based on Shannon Entropy
    (Springer, 2023-09-22) Navarro, Jorge; Buono, Francesco; Martín Arevalillo, Jorge; https://orcid.org/0000-0003-2822-915X; https://orcid.org/0000-0002-3569-4052
    The purpose is to use Shannon entropy measures to develop classification techniques and an index which estimates the separation of the groups in a finite mixture model. These measures can be applied to machine learning techniques such as discriminant analysis, cluster analysis, exploratory data analysis, etc. If we know the number of groups and we have training samples from each group (supervised learning) the index is used to measure the separation of the groups. Here some entropy measures are used to classify new individuals in one of these groups. If we are not sure about the number of groups (unsupervised learning), the index can be used to determine the optimal number of groups from an entropy (information/uncertainty) criterion. It can also be used to determine the best variables in order to separate the groups. In all the cases we assume that we have absolutely continuous random variables and we use the Shannon entropy based on the probability density function. Theoretical, parametric and non-parametric techniques are proposed to get approximations of these entropy measures in practice. An application to gene selection in a colon cancer discrimination study with a lot of variables is provided as well.
  • Miniatura
    Publicación
    On connections between skewed, weighted and distorted distributions: applications to model extreme value distributions
    (Springer, 2023-08-05) Navarro, Jorge; Martín Arevalillo, Jorge
    The purpose of the paper is to explore the connections between skew symmetric, weighted and distorted univariate distributions as well as how they appear related to the distributions of the extreme values in a sample of identically distributed random variables under both the independence and dependence scenarios. Some extensions of the concept of skewed distributions are proposed in order to cover the most general cases of extremes. Their natural connections to the likelihood ratio ordering and the role played by the P–P plots for handling these models are also highlighted. The results can also be applied to order statistics and coherent systems although these cases do not always lead to skewed distributions. The theoretical findings are illustrated by applied examples to model extremes as well as by several applications concerned with the analysis of artificial and real data.
  • Miniatura
    Publicación
    Assessment of extreme records in environmental data through the study of stochastic orders for scale mixtures of skew normal vectors
    (Springer, 2024-02-18) Martín Arevalillo, Jorge; Navarro, Jorge
    Scale mixtures of skew normal distributions are flexible models well-suited to handle departures from multivariate normality. This paper is concerned with the stochastic comparison of vectors that belong to the family of scale mixtures of skew normal distributions. The paper revisits some of their properties with a proposal that allows to carry out tail weight stochastic comparisons. The connections of the proposed stochastic orders with the non-normality parameters of the multivariate model are also studied for some popular distributions within the family. The role played by these parameters to tackle the non-normality of multivariate data is enhanced as a result. This work is motivated by the analysis of multivariate data in environmental studies which usually collect maximum or minimum values exhibiting departures from normality. The implications of our theoretical results in addressing the stochastic comparison of extreme environmental records is illustrated with an application to a real data study on maximum temperatures in the Iberian Peninsula throughout the last century. The resulting findings may elucidate whether extreme temperatures are evolving for such a long period.