Copula modeling from Abe Sklar to the present day

Genest, Christian; Okhrin, Ostap; Bodnar, Taras

doi:10.1016/j.jmva.2023.105278

Cited by 2 publications

(4 citation statements)

References 180 publications

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“…Then, (1) follows immediately from ( 2) and ( 3). Evidently, the values taken by any such copula C outside Ś d k=1 Ran F k are totally irrelevant, as they do not even appear in (1). All in all, Théorème 2 is akin to part 1(i) of Theorem 0, while, clearly, Théorème 3 is its part 2.…”

Section: Sklar's Statementsmentioning

confidence: 99%

“…It is, therefore, my opinion that copula-like methods for analysing, modelling and quantifying dependence in non-continuous multivariate distributions should not be based on (1). I elaborated on this in [10], and proposed an alternative approach for discrete distributions.…”

Section: Some Personal Commentsmentioning

confidence: 99%

“…In probability and statistics, copula methods have become ubiquitous when it comes to analysing, modelling and quantifying the dependence between variables; Genest et al [1] provides a comprehensive up-to-date literature review on copula methods for approaching dependence in a variety of statistical settings. Systematically, any written (research paper) or verbal (conference talk) communication about copulas starts with a statement of the socalled 'Sklar's theorem', establishing the existence of a copula for any multivariate probability distribution.…”

Section: Introductionmentioning

confidence: 99%

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(Re-)Reading Sklar (1959)—A Personal View on Sklar’s Theorem

Geenens

2024

Mathematics

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In this short communication, I share some personal thoughts on Sklar’s theorem and copulas after reading the original paper (Sklar, 1959) in French. After providing a literal translation of Sklar’s original statements, I argue that the modern version of `Sklar’s theorem’ given in most references has a slightly different emphasis, which may lead to subtly different interpretations. In particular, with no reference to the subcopula, modern `Sklar’s theorem’ does not provide the clues to fully appreciate when the copula representation of a distribution may form a valid basis for dependence modelling and when it may not.

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Section: Sklar's Statementsmentioning

confidence: 99%

Section: Some Personal Commentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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(Re-)Reading Sklar (1959)—A Personal View on Sklar’s Theorem

Geenens

2024

Mathematics

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“…

and

represent the cumulative distribution functions (CDFs) of the two wind vector variables, respectively, and their joint cumulative distribution function (JCDF) is denoted as F ( x , θ ). In accordance with Sklar’s theorem [ 46 ], the relationship between wind speed and direction could be expressed with a correlation function

since

, then

. The JPDF of wind speed and direction is expressed as the following equation:

…”

Section: Nonparametric Probabilistic Modelmentioning

confidence: 99%

A Circular-Linear Probabilistic Model Based on Nonparametric Copula with Applications to Directional Wind Energy Assessment

Liu,

Yan

2024

Entropy

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The joint probability density function of wind speed and wind direction serves as the mathematical basis for directional wind energy assessment. In this study, a nonparametric joint probability estimation system for wind velocity and direction based on copulas is proposed and empirically investigated in Inner Mongolia, China. Optimal bandwidth algorithms and transformation techniques are used to determine the nonparametric copula method. Various parameter copula models and models without considering dependency relationships are introduced and compared with this approach. The results indicate a significant advantage of employing the nonparametric copula model for fitting joint probability distributions of both wind speed and wind direction, as well as conducting correlation analyses. By utilizing the proposed KDE-COP-CV model, it becomes possible to accurately and reliably analyze how wind power density fluctuates in relation to wind direction. This study reveals the researched region possesses abundant wind resources, with the highest wind power density being highly dependent on wind direction at maximum speeds. Wind resources in selected regions of Inner Mongolia are predominantly concentrated in the northwest and west directions. These findings can contribute to improving the accuracy of micro-siting for wind farms, as well as optimizing the design and capacity of wind turbine generators.

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Copula modeling from Abe Sklar to the present day

Cited by 2 publications

References 180 publications

(Re-)Reading Sklar (1959)—A Personal View on Sklar’s Theorem

(Re-)Reading Sklar (1959)—A Personal View on Sklar’s Theorem

A Circular-Linear Probabilistic Model Based on Nonparametric Copula with Applications to Directional Wind Energy Assessment

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