Symmetric Bernoulli distributions and minimal dependence copulas
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913899467505664 |
|---|---|
| author | Mutti, Alessandro Semeraro, Patrizia |
| author_facet | Mutti, Alessandro Semeraro, Patrizia |
| contents | The key result of this paper is to characterize all the multivariate symmetric Bernoulli distributions whose sum is minimal under convex order. In doing so, we automatically characterize extremal negative dependence among Bernoulli random vectors, since multivariate distributions with minimal convex sums are known to be strongly negative dependent. Moreover, beyond its interest per se, this result provides insight into negative dependence within the class of copulas. In particular, two classes of copulas can be built from multivariate symmetric Bernoulli distributions: extremal mixture copulas and FGM copulas. We analyze the extremal negative dependence structures of copulas corresponding to symmetric Bernoulli random vectors with minimal convex sums and explicitly find a class of minimal dependence copulas. Our main results derive from the geometric and algebraic representations of multivariate symmetric Bernoulli distributions, which effectively encode key statistical properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_17346 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Symmetric Bernoulli distributions and minimal dependence copulas Mutti, Alessandro Semeraro, Patrizia Statistics Theory Mathematical Finance The key result of this paper is to characterize all the multivariate symmetric Bernoulli distributions whose sum is minimal under convex order. In doing so, we automatically characterize extremal negative dependence among Bernoulli random vectors, since multivariate distributions with minimal convex sums are known to be strongly negative dependent. Moreover, beyond its interest per se, this result provides insight into negative dependence within the class of copulas. In particular, two classes of copulas can be built from multivariate symmetric Bernoulli distributions: extremal mixture copulas and FGM copulas. We analyze the extremal negative dependence structures of copulas corresponding to symmetric Bernoulli random vectors with minimal convex sums and explicitly find a class of minimal dependence copulas. Our main results derive from the geometric and algebraic representations of multivariate symmetric Bernoulli distributions, which effectively encode key statistical properties. |
| title | Symmetric Bernoulli distributions and minimal dependence copulas |
| topic | Statistics Theory Mathematical Finance |
| url | https://arxiv.org/abs/2309.17346 |