Bivariate measure-inducing quasi-copulas
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929304103813120 |
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| author | Stopar, Nik |
| author_facet | Stopar, Nik |
| contents | It is well known that every bivariate copula induces a positive measure on the Borel $σ$-algebra on $[0,1]^2$, but there exist bivariate quasi-copulas that do not induce a signed measure on the same $σ$-algebra. In this paper we show that a signed measure induced by a bivariate quasi-copula can always be expressed as an infinite combination of measures induced by copulas. With this we are able to give the first characterization of measure-inducing quasi-copulas in the bivariate setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04560 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bivariate measure-inducing quasi-copulas Stopar, Nik Statistics Theory Probability 62H05, 60B10, 60A10 It is well known that every bivariate copula induces a positive measure on the Borel $σ$-algebra on $[0,1]^2$, but there exist bivariate quasi-copulas that do not induce a signed measure on the same $σ$-algebra. In this paper we show that a signed measure induced by a bivariate quasi-copula can always be expressed as an infinite combination of measures induced by copulas. With this we are able to give the first characterization of measure-inducing quasi-copulas in the bivariate setting. |
| title | Bivariate measure-inducing quasi-copulas |
| topic | Statistics Theory Probability 62H05, 60B10, 60A10 |
| url | https://arxiv.org/abs/2404.04560 |