Stochastic representation of FGM copulas using multivariate Bernoulli random variables

Blier-Wong, Christopher; Cossette, Hélène; Marceau, Étienne

doi:10.1016/j.csda.2022.107506

Cited by 9 publications

(22 citation statements)

References 24 publications

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“…}, which is also the case for the EPD copula. As noted in Blier-Wong et al (2022), the dependence parameters for odd indices do not contribute to the overall strength of dependence.…”

Section: Supermodular Ordering Within Efgm Copulasmentioning

confidence: 80%

“…, θ d ) in (4) becomes tedious. A preferable approach will rely on the following stochastic representation introduced in Blier- Wong et al (2022).…”

Section: Definitionmentioning

confidence: 99%

“…The following theorem from Blier-Wong et al (2022) presents the general result for supermodular orders within FGM copulas with the stochastic representation.…”

Section: Supermodular Ordering Within Efgm Copulasmentioning

confidence: 99%

“…In Blier-Wong et al (2022), an efficient stochastic sampling method is proposed based on the stochastic representation of FGM copulas. In Algorithm 1, we leverage the representation based on the class N d from Subsection 3.1 to efficiently sample observations from eFGM copulas.…”

Section: Samplingmentioning

confidence: 99%

“…In Blier-Wong et al (2022), the authors establish a one-to-one correspondence between FGM copulas and symmetric multivariate Bernoulli distributions. One advantage of this representation is that one may construct subfamilies of FGM copulas by selecting subfamilies of multivariate symmetric Bernoulli distributions.…”

Section: Introductionmentioning

confidence: 99%

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Exchangeable FGM copulas

Blier-Wong¹,

Cossette²,

Marceau³

2022

Preprint

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Copulas are a powerful tool to model dependence between the components of a random vector. One well-known class of copulas when working in two dimensions is the Farlie-Gumbel-Morgenstern (FGM) copula since their simple analytic shape enables closed-form solutions to many problems in applied probability. However, the classical definition of high-dimensional FGM copula does not enable a straightforward understanding of the effect of the copula parameters on the dependence, nor a geometric understanding of their admissible range. We circumvent this issue by studying the FGM copula from a probabilistic approach based on multivariate Bernoulli distributions. This paper studies high-dimensional exchangeable FGM copulas, a subclass of FGM copulas. We show that dependence parameters of exchangeable FGM can be expressed as convex hulls of a finite number of extreme points and establish partial orders for different exchangeable FGM copulas (including maximal and minimal dependence). We also leverage the probabilistic interpretation to develop efficient sampling and estimating procedures and provide a simulation study. Throughout, we discover geometric interpretations of the copula parameters that assist one in decoding the dependence of high-dimensional exchangeable FGM copulas.

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“…}, which is also the case for the EPD copula. As noted in Blier-Wong et al (2022), the dependence parameters for odd indices do not contribute to the overall strength of dependence.…”

Section: Supermodular Ordering Within Efgm Copulasmentioning

confidence: 80%

“…, θ d ) in (4) becomes tedious. A preferable approach will rely on the following stochastic representation introduced in Blier- Wong et al (2022).…”

Section: Definitionmentioning

confidence: 99%

“…The following theorem from Blier-Wong et al (2022) presents the general result for supermodular orders within FGM copulas with the stochastic representation.…”

Section: Supermodular Ordering Within Efgm Copulasmentioning

confidence: 99%

Section: Samplingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Exchangeable FGM copulas

Blier-Wong¹,

Cossette²,

Marceau³

2022

Preprint

Self Cite

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Intelligent Control for Floating Offshore Wind Turbines Based on Game Theory with Data‐Driven and Reliability Awareness

Zhang

Yang

2023

Energy Tech

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To address the challenges of complex modeling and control objective conflicts, a game control scheme based on data‐driven and reliability awareness is proposed for floating offshore wind turbines (FOWTs). In this scheme, first, an enhanced model‐free adaptive control method with the integration of iterative learning is proposed, which utilized online data for driving modeling and control command derivation to ensure the functionality of the FOWT and maintain stable power generation. Then, a healthy reliability‐aware model of the pitching system is developed and integrated into the controller of FOWTs. Finally, a trade‐off between the reliability and functionality of FOWTs is intelligently made through bargaining game theory to derive reasonable control commands. Simulation experiments of the proposed control scheme are carried out using FAST under different wind conditions. The results show that, compared with the gain‐scheduled PI controller and model‐free adaptive controller, the output power of the proposed controller is more stable and the pitch motion of the FOWT is significantly reduced; compared with the improved model‐free adaptive controller, the proposed controller improves the reliability of the pitch system.

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