A new method to construct high-dimensional copulas with Bernoulli and Coxian-2 distributions Article Swipe
Christopher Blier-Wong
,
Hélène Cossette
,
Sébastien Legros
,
Étienne Marceau
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2209.13675
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2209.13675
We propose an approach to construct a new family of generalized Farlie-Gumbel-Morgenstern (GFGM) copulas that naturally scales to high dimensions. A GFGM copula can model moderate positive and negative dependence, cover different types of asymmetries, and admits exact expressions for many quantities of interest such as measures of association or risk measures in actuarial science or quantitative risk management. More importantly, this paper presents a new method to construct high-dimensional copulas based on mixtures of power functions, and may be adapted to more general contexts to construct broader families of copulas. We construct a family of copulas through a stochastic representation based on multivariate Bernoulli distributions and Coxian-2 distributions. This paper will cover the construction of a GFGM copula, study its measures of multivariate association and dependence properties. We explain how to sample random vectors from the new family of copulas in high dimensions. Then, we study the bivariate case in detail and find that our construction leads to an asymmetric modified Huang-Kotz FGM copula. Finally, we study the exchangeable case and provide some insights into the most negative dependence structure within this new class of high-dimensional copulas.
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- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2209.13675
- https://arxiv.org/pdf/2209.13675
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4298051048
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Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4298051048Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2209.13675Digital Object Identifier
- Title
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A new method to construct high-dimensional copulas with Bernoulli and Coxian-2 distributionsWork title
- Type
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preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2022Year of publication
- Publication date
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2022-09-27Full publication date if available
- Authors
-
Christopher Blier-Wong, Hélène Cossette, Sébastien Legros, Étienne MarceauList of authors in order
- Landing page
-
https://arxiv.org/abs/2209.13675Publisher landing page
- PDF URL
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https://arxiv.org/pdf/2209.13675Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2209.13675Direct OA link when available
- Concepts
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Copula (linguistics), Bivariate analysis, Construct (python library), Bernoulli's principle, Multivariate statistics, Mathematics, Econometrics, Tail dependence, Applied mathematics, Statistical physics, Computer science, Statistics, Physics, Programming language, ThermodynamicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.importantly, | 60 |
| abstract_inverted_index.multivariate | 103, 123 |
| abstract_inverted_index.quantitative | 56 |
| abstract_inverted_index.distributions | 105 |
| abstract_inverted_index.distributions. | 108 |
| abstract_inverted_index.representation | 100 |
| abstract_inverted_index.high-dimensional | 69, 186 |
| abstract_inverted_index.Farlie-Gumbel-Morgenstern | 11 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 4 |
| citation_normalized_percentile |