TY - UNPB
T1 - Correlation-based and-operations can be copulas
T2 - a proof
AU - Miralles-Dolz, Enrique
AU - Gray, Ander
AU - Patelli, Edoardo
AU - Ferson, Scott
AU - Kreinovich, Vladik
AU - Kosheleva, Olga
PY - 2023/1/13
Y1 - 2023/1/13
N2 - 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.
AB - 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.
KW - joint probability
KW - and-operation
KW - copulas
U2 - 10.48550/arXiv.2301.05507
DO - 10.48550/arXiv.2301.05507
M3 - Working Paper/Preprint
BT - Correlation-based and-operations can be copulas
CY - Ithaca, NY
ER -