ON THE EXTREMAL DEPENDENCE COEFFICIENTS OF GAUSSIAN DISTRIBUTIONS
S.E. Khrushchev
Novosibirsk State University of Economics and Management, Novosibirsk, Russian Federation
Keywords: copula, Gaussian distribution, extremal dependence coefficients, COVID-19 coronavirus infection
Abstract
The paper considers a way to represent the relationship between indicators in the form of copulas. Copulas are popular mathematical tools. This is due to the fact that, on the one hand, the marginal distributions of indicators are divided in the copulas, and on the other hand, the structure of the relationship between these marginal distributions is divided, which makes it possible to very effectively study the connections that arise in real populations. Special attention in the work is paid to extremal dependence coefficients - important numerical characteristics of the connection in conditions of extreme small or extremely large values of indicators. It is shown that even under conditions of close correlation between the indices for a two-dimensional Gaussian distribution, the lower and upper coefficients of the extreme dependence take zero values. This indicates the impossibility of predicting the values of one indicator when fixing too small or too large values of another indicator. This work shows that the relationship between the number of COVID-19 coronavirus infections per 100,000 people and the number of deaths from COVID-19 coronavirus infection per 100,000 people in the regions of the Russian Federation can be represented in the form of a Gaussian copula.
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