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Mathematics
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Dependence Modeling with Copulas and Their Applications
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Dependence Modeling with Copulas and Their Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D1: Probability and Statistics".

Deadline for manuscript submissions: closed (30 June 2024) | Viewed by 6203

Special Issue Editors

Prof. Dr. Manuel Úbeda-Flores

E-Mail Website
Guest Editor
Department of Mathematics, University of Almería, 04120 Almería, Spain
Interests: copula; dependence modeling
Prof. Dr. Enrique de Amo

E-Mail Website
Guest Editor
Department of Mathematics, University of Almería, 04120 Almería, Spain
Interests: copula; dependence modeling

Special Issue Information

Dear Colleagues,

In probability and statistics, a copula is a multivariate cumulative distribution function for which the marginal probability distribution of each variable is uniform on the interval [0, 1]. Copulas are used to describe or model the dependence between random variables. They were introduced by Abe Sklar in 1959, and the word comes from the Latin for "link" or "tie", since they relate a multivariate distribution function to its one-dimensional marginals. Copulas have been used widely in quantitative finance to model and minimize tail risk and portfolio-optimization applications.

Copulas are popular in high-dimensional statistical applications as they allow one to easily model and estimate the distribution of random vectors by estimating marginals and copulas separately. There are many parametric copula families available, which usually have parameters that control the strength of dependence.

This Special Issue, ‘Dependence Modeling with Copulas and Their Applications’, aims to collate original research articles as well as comprehensive reviews addressing the theories and applications of copulas in quantitative finance, reliability, hydrology, computer science, etc.

Prof. Dr. Manuel Úbeda-Flores
Prof. Dr. Enrique de Amo
Guest Editors

Manuscript Submission Information

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Keywords

  • copula
  • quasi-copula
  • dependence models
  • measures of association
  • stochastic ordering
  • extreme value analysis
  • quantitative finance

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Published Papers (5 papers)

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Research

27 pages, 574 KiB  
Article
Modelling the Dependence between a Wiener Process and Its Running Maxima and Running Minima Processes
by Karol Da̧browski and Piotr Jaworski
Mathematics 2024, 12(17), 2707; https://doi.org/10.3390/math12172707 - 30 Aug 2024
Viewed by 783
Abstract
We study a triple of stochastic processes: a Wiener process Wt, t≥0, its running maxima process Mt=sup{Ws:s∈[0,t]}, and its running minima process [...] Read more.
We study a triple of stochastic processes: a Wiener process Wt, t≥0, its running maxima process Mt=sup{Ws:s∈[0,t]}, and its running minima process mt=inf{Ws:s∈[0,t]}. We derive the analytical formula for the corresponding copula and show that it is supported on the hemicube, a convex hexahedron with seven vertices. As an application, we draw out an analytical formula for pricing of a double barrier option. Full article
(This article belongs to the Special Issue Dependence Modeling with Copulas and Their Applications)
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35 pages, 1772 KiB  
Article
Advanced Copula-Based Models for Type II Censored Data: Applications in Industrial and Medical Settings
by Ehab M. Almetwally, Aisha Fayomi and Maha E. Qura
Mathematics 2024, 12(12), 1774; https://doi.org/10.3390/math12121774 - 7 Jun 2024
Cited by 3 | Viewed by 1328
Abstract
Copula models are increasingly recognized for their ability to capture complex dependencies among random variables. In this study, we introduce three innovative bivariate models utilizing copula functions: the XLindley (XL) distribution with Frank, Gumbel, and Clayton copulas. The results highlight the fundamental characteristics [...] Read more.
Copula models are increasingly recognized for their ability to capture complex dependencies among random variables. In this study, we introduce three innovative bivariate models utilizing copula functions: the XLindley (XL) distribution with Frank, Gumbel, and Clayton copulas. The results highlight the fundamental characteristics and effectiveness of these newly introduced bivariate models. Statistical inference for the distribution parameters is conducted using a Type II censored sampling design. This employs maximum likelihood and Bayesian estimation techniques. Asymptotic and credible confidence intervals are calculated, and numerical analysis is performed using the Markov Chain Monte Carlo method. The proposed methodology’s applicability is illustrated by analyzing several real-world datasets. The initial dataset examines burr formation occurrences and consists of two observation sets. Additionally, the second and third datasets contain medical information. The second dataset focuses on diabetic nephropathy, while the third dataset explores infection and recurrence time among kidney patients. Full article
(This article belongs to the Special Issue Dependence Modeling with Copulas and Their Applications)
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17 pages, 1341 KiB  
Article
On the Ratio-Type Family of Copulas
by Farid El Ktaibi, Rachid Bentoumi and Mhamed Mesfioui
Mathematics 2024, 12(11), 1743; https://doi.org/10.3390/math12111743 - 3 Jun 2024
Viewed by 787
Abstract
Investigating dependence structures across various fields holds paramount importance. Consequently, the creation of new copula families plays a crucial role in developing more flexible stochastic models that address the limitations of traditional and sometimes impractical assumptions. The present article derives some reasonable conditions [...] Read more.
Investigating dependence structures across various fields holds paramount importance. Consequently, the creation of new copula families plays a crucial role in developing more flexible stochastic models that address the limitations of traditional and sometimes impractical assumptions. The present article derives some reasonable conditions for validating a copula of the ratio-type form uv/(1−θf(u)g(v)). It includes numerous examples and discusses the admissible range of parameter θ, showcasing the diversity of copulas generated through this framework, such as Archimedean, non-Archimedean, positive dependent, and negative dependent copulas. The exploration extends to the upper bound of a general family of copulas, uv/(1−θϕ(u,v)), and important properties of the copula are discussed, including singularity, measures of association, tail dependence, and monotonicity. Furthermore, an extensive simulation study is presented, comparing the performance of three different estimators based on maximum likelihood, ρ-inversion, and the moment copula method. Full article
(This article belongs to the Special Issue Dependence Modeling with Copulas and Their Applications)
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14 pages, 294 KiB  
Article
Directional Dependence Orders of Random Vectors
by Enrique de Amo, María del Rosario Rodríguez-Griñolo and Manuel Úbeda-Flores
Mathematics 2024, 12(3), 419; https://doi.org/10.3390/math12030419 - 27 Jan 2024
Cited by 2 | Viewed by 997
Abstract
In this paper, we define a multivariate order based on the concept of orthant directional dependence and study some of its properties. The relationships with other dependence orders given in the literature are also studied. We analyze the order between two random vectors [...] Read more.
In this paper, we define a multivariate order based on the concept of orthant directional dependence and study some of its properties. The relationships with other dependence orders given in the literature are also studied. We analyze the order between two random vectors in terms of their associated copulas and illustrate our results with several examples. Full article
(This article belongs to the Special Issue Dependence Modeling with Copulas and Their Applications)
18 pages, 1221 KiB  
Article
A New Family of Archimedean Copulas: The Half-Logistic Family of Copulas
by Abdulhamid A. Alzaid and Weaam M. Alhadlaq
Mathematics 2024, 12(1), 101; https://doi.org/10.3390/math12010101 - 27 Dec 2023
Cited by 4 | Viewed by 1611
Abstract
In this research, we introduce a truncation of the half-logistic distribution function as a multiplicative Archimedean generator. The corresponding Archimedean copula is obtained, namely the half-logistic family. The dependency structure of this copula is distinct from other well-known ones. Kendall’s tau correlation coefficient [...] Read more.
In this research, we introduce a truncation of the half-logistic distribution function as a multiplicative Archimedean generator. The corresponding Archimedean copula is obtained, namely the half-logistic family. The dependency structure of this copula is distinct from other well-known ones. Kendall’s tau correlation coefficient is obtained in exact form and found to cover the entire positive dependence range (i.e., [0, 1]). We have proven that this copula is positively ordered and has no tail dependencies. The density of this copula is shown to be totally positive of order two. An extension of this copula is also introduced by adding a second parameter. This extension allows for a negative correlation and connects the famous Frank copula to the half-logistic copula. Two datasets were used to compare the half-logistic copula with some other known copula models. Full article
(This article belongs to the Special Issue Dependence Modeling with Copulas and Their Applications)
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