Correlation-based and-operations can be copulas : a proof
Miralles-Dolz, Enrique and Gray, Ander and Patelli, Edoardo and Ferson, Scott and Kreinovich, Vladik and Kosheleva, Olga (2023) Correlation-based and-operations can be copulas : a proof. Other. arXiv, Ithaca, NY. (https://doi.org/10.48550/arXiv.2301.05507)
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Abstract
In many practical situations, we know the probabilities a and b of two events A and B, and we want to estimate the joint probability Prob(A & B). The algorithm that estimates the joint probability based on the known values a and b is called an and-operation. An important case when such a reconstruction is possible is when we know the correlation between A and B; we call the resulting and-operation correlation-based. On the other hand, in statistics, there is a widely used class of and-operations known as copulas. Empirical evidence seems to indicate that the correlation-based and-operation derived in https://doi.org/10.1007/978-3-031-08971-8_64 is a copula, but until now, no proof of this statement was available. In this paper, we provide such a proof.
ORCID iDs
Miralles-Dolz, Enrique, Gray, Ander, Patelli, Edoardo ORCID: https://orcid.org/0000-0002-5007-7247, Ferson, Scott, Kreinovich, Vladik and Kosheleva, Olga;-
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Item type: Monograph(Other) ID code: 90447 Dates: DateEvent13 January 2023PublishedSubjects: Science > Mathematics > Probabilities. Mathematical statistics Department: Faculty of Engineering > Civil and Environmental Engineering Depositing user: Pure Administrator Date deposited: 03 Sep 2024 08:42 Last modified: 04 Sep 2024 01:24 URI: https://strathprints.strath.ac.uk/id/eprint/90447