A new asymmetric class of bivariate copulas for modeling dependence

Bekrizadeh, Hakim; Parham, Gholam Ali; Jamshidi, Babak

doi:10.1080/03610918.2016.1169292

Cited by 13 publications

(8 citation statements)

References 10 publications

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“…Furthermore, these Archimedean copulas allow simple formulas to compute the CG estimators [ 52 ]. However, there are a large number of non-Archimedean copulas popular in a variety of applications, such as the FGM copula, Gaussian copula, trigonometric copula, and Celebioglu–Cuadras copula [ 82 , 83 , 84 , 85 , 86 , 87 ]. As the CG estimators have not been considered for these non-Archimedean copulas, it is of great interest to develop computational tools for them.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Sensitivity Analysis for Survival Prognostic Prediction with Gene Selection: A Copula Method for Dependent Censoring

2023

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Prognostic analysis for patient survival often employs gene expressions obtained from high-throughput screening for tumor tissues from patients. When dealing with survival data, a dependent censoring phenomenon arises, and thus the traditional Cox model may not correctly identify the effect of each gene. A copula-based gene selection model can effectively adjust for dependent censoring, yielding a multi-gene predictor for survival prognosis. However, methods to assess the impact of various types of dependent censoring on the multi-gene predictor have not been developed. In this article, we propose a sensitivity analysis method using the copula-graphic estimator under dependent censoring, and implement relevant methods in the R package “compound.Cox”. The purpose of the proposed method is to investigate the sensitivity of the multi-gene predictor to a variety of dependent censoring mechanisms. In order to make the proposed sensitivity analysis practical, we develop a web application. We apply the proposed method and the web application to a lung cancer dataset. We provide a template file so that developers can modify the template to establish their own web applications.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Sensitivity Analysis for Survival Prognostic Prediction with Gene Selection: A Copula Method for Dependent Censoring

2023

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“…See, for instance, Ref. [19] (Example 2.2), [20] (Example 2), [21] (Example 5), and [22] (Example 2). However, to the best of our knowledge, despite the immediate advantages of this copula, there is not much attention given to it.…”

Section: Introductionmentioning

confidence: 99%

“…Our methodology follows the power generalization schemes proposed in [23], where three-parameter-power-type generalizations of the FGM copula are discussed. To be more precise, our proposed copulas are of the following forms: Some of these generalized forms have been sketched in [19,22], but only for specific values of a, b, and c. To the best of our knowledge, no global studies exist, and this paper aims to fill this gap. Thus, the main challenge of this study is to determine wide and manageable admissible domains of values for a, b, and c so that copulas of these forms remain mathematically valid.…”

Section: Introductionmentioning

confidence: 99%

Theoretical Contributions to Three Generalized Versions of the Celebioglu–Cuadras Copula

Chesneau

2023

Analytics

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Copulas are probabilistic functions that are being used more and more frequently to describe, examine, and model the interdependence of continuous random variables. Among the numerous proposed copulas, renewed interest has recently been shown in the so-called Celebioglu–Cuadras copula. It is mainly because of its simplicity, exploitable dependence properties, and potential for applicability. In this article, we contribute to the development of this copula by proposing three generalized versions of it, each involving three tuning parameters. The main results are theoretical: they consist of determining wide and manageable intervals of admissible values for the involved parameters. The proofs are mainly based on limit, differentiation, and factorization techniques as well as mathematical inequalities. Some of the configuration parameters are new in the literature, and original phenomena are revealed. Subsequently, the basic properties of the proposed copulas are studied, such as symmetry, quadrant dependence, various expansions, concordance ordering, tail dependences, medial correlation, and Spearman correlation. Detailed examples, numerical tables, and graphics are used to support the theory.

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“…As a result, many authors have devised novel strategies for producing copulas with unique forms and manageable dependence properties. See [10][11][12][13][14][15][16][17][18][19][20][21], among others. In particular, the contemporary works of [14,17] have attracted our attention.…”

Section: Introductionmentioning

confidence: 99%

Theoretical Advancements on a Few New Dependence Models Based on Copulas with an Original Ratio Form

Chesneau

2023

Modelling

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Copulas are well-known tools for describing the relationship between two or more quantitative variables. They have recently received a lot of attention, owing to the variable dependence complexity that appears in heterogeneous modern problems. In this paper, we offer five new copulas based on a common original ratio form. All of them are defined with a single tuning parameter, and all reduce to the independence copula when this parameter is equal to zero. Wide admissible domains for this parameter are established, and the mathematical developments primarily rely on non-trivial limits, two-dimensional differentiations, suitable factorizations, and mathematical inequalities. The corresponding functions and characteristics of the proposed copulas are looked at in some important details. In particular, as common features, it is shown that they are diagonally symmetric, but not Archimedean, not radially symmetric, and without tail dependence. The theory is illustrated with numerical tables and graphics. A final part discusses the multi-dimensional variation of our original ratio form. The contributions are primarily theoretical, but they provide the framework for cutting-edge dependence models that have potential applications across a wide range of fields. Some established two-dimensional inequalities may be of interest beyond the purposes of this paper.

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A new asymmetric class of bivariate copulas for modeling dependence

Cited by 13 publications

References 10 publications

Sensitivity Analysis for Survival Prognostic Prediction with Gene Selection: A Copula Method for Dependent Censoring

Sensitivity Analysis for Survival Prognostic Prediction with Gene Selection: A Copula Method for Dependent Censoring

Theoretical Contributions to Three Generalized Versions of the Celebioglu–Cuadras Copula

Theoretical Advancements on a Few New Dependence Models Based on Copulas with an Original Ratio Form

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