A New Family of Archimedean Copula via Trigonometric Generator Function

Susam, Selim Orhun

doi:10.35378/gujs.635032

Cited by 11 publications

(13 citation statements)

References 11 publications

(11 reference statements)

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“…In the spirit of [30,31], it needs to demonstrate the goodness of fit performance of the new copulas using real data analysis; • Beyond probability and statistics, one can think of applying the proposed copulas in mathematical physics, as in the topics considered in [36][37][38]; • In view of the established theory, one can also think of constructing a new measure of correlation that fully takes into account the oscillating nature of the multivariate trigonometric copulas, following the ideas developed in [32].…”

Section: Concluding Remarks and Perspectivesmentioning

confidence: 99%

“…In particular, highlighted copulas that involve trigonometric functions are rare, despite a certain potential for applications. The most famous trigonometric copulas are the simple sine (SS) copulas, exemplified in ( [25], Example 1 (point 4)) and ( [26], Example 5), then further studied in [27], the sine-type copulas created by [28], the polynomial cosine copula introduced by [29], and the trigonometric archimedean copulas developed by [30,31]. The appeal of such copulas is that the trigonometric function's oscillating features can be used to describe various variable dependence structures that non-trigonometric copulas cannot.…”

Section: Introductionmentioning

confidence: 99%

“…In the two dimensional case, we can think of the analysis of data as presenting scatter plots with oscillating patterns. The practical benefit is especially apparent when analyzing multivariate environmental data, such as those investigated by [30,31].…”

Section: Introductionmentioning

confidence: 99%

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On New Types of Multivariate Trigonometric Copulas

Chesneau

2021

AppliedMath

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Copulas are useful functions for modeling multivariate distributions through their univariate marginal distributions and dependence structures. They have a wide range of applications in all fields of science that deal with multivariate data. While there is a plethora of copulas, those based on trigonometric functions, especially in dimensions greater than two, have received much less attention. They are, however, of interest because of the properties of oscillation and periodicity of the trigonometric functions, which can appear in certain models of correlation of natural phenomena. In order to fill this gap, this paper introduces and investigates two new types of “multivariate trigonometric copulas”. Their main theoretical properties are studied, and some perspectives for applications are sketched for future work. In particular, we show that the proposed copulas are symmetric, not associative, with no orthant dependence, and with copula densities that have wide oscillations, which remains an uncommon property in the field. The expressions of their multivariate Spearman’s rho are also determined. Furthermore, the first type of the proposed copulas has the interesting feature of having a multivariate Spearman’s rho equal to 0 for all of the dimensions. Some graphic evidence supports the findings. Some mathematical formulas involving the product of n trigonometric functions may be of independent interest.

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Section: Concluding Remarks and Perspectivesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On New Types of Multivariate Trigonometric Copulas

Chesneau

2021

AppliedMath

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“…The theory of the classical trigonometric copulas can be found in [5][6][7][8][9][10][11]. For practice, we refer to [12][13][14][15][16]. Furthermore, the R package named Cylcop, recently developed by [17], gives the trigonometric (and circular) copulas a new dimension of applicability.…”

Section: Introductionmentioning

confidence: 99%

“…The use of the sin-copula and cos-copula for data analysis, following the methodology in [13,15], is an important perspective. Furthermore, the development of an R package is envisageable, inspired by the research design of Cylcop developed by [17].…”

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confidence: 99%

Theoretical Study of Some Angle Parameter Trigonometric Copulas

Chesneau

2022

Modelling

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Copulas are important probabilistic tools to model and interpret the correlations of measures involved in real or experimental phenomena. The versatility of these phenomena implies the need for diverse copulas. In this article, we describe and investigate theoretically new two-dimensional copulas based on trigonometric functions modulated by a tuning angle parameter. The independence copula is, thus, extended in an original manner. Conceptually, the proposed trigonometric copulas are ideal for modeling correlations into periodic, circular, or seasonal phenomena. We examine their qualities, such as various symmetry properties, quadrant dependence properties, possible Archimedean nature, copula ordering, tail dependences, diverse correlations (medial, Spearman, and Kendall), and two-dimensional distribution generation. The proposed copulas are fleshed out in terms of data generation and inference. The theoretical findings are supplemented by some graphical and numerical work. The main results are proved using two-dimensional inequality techniques that can be used for other copula purposes.

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On the Gumbel–Barnett extended Celebioglu–Cuadras copula

Chesneau

2023

Jpn J Stat Data Sci

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A New Family of Archimedean Copula via Trigonometric Generator Function

Abstract: Highlights • A new type of Archimedean copula is proposed. • Proposed copula covers wider dependence coefficients interval. • We investigated the estimation of the parameter of cotangent copula. • Cotangent copula can lead to better fits for real data.

Cited by 11 publications

References 11 publications

On New Types of Multivariate Trigonometric Copulas

On New Types of Multivariate Trigonometric Copulas

Theoretical Study of Some Angle Parameter Trigonometric Copulas

On the Gumbel–Barnett extended Celebioglu–Cuadras copula

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