Extremal Dependence Concepts

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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On the distance between convex-ordered random variables, with applications

Advances in Applied Probability ◽

10.1239/aap/1025131222 ◽

2002 ◽

Vol 34 (2) ◽

pp. 349-374 ◽

Cited By ~ 14

Author(s):

Michael V. Boutsikas ◽

Eutichia Vaggelatou

Keyword(s):

Random Variables ◽

Simple Approximation ◽

Negative Dependence ◽

Exponential Approximation ◽

Probability Metrics ◽

Convex Ordering ◽

Compound Poisson ◽

Approximation Techniques ◽

Negatively Dependent Random Variables ◽

Dependence Concepts

Simple approximation techniques are developed exploiting relationships between generalized convex orders and appropriate probability metrics. In particular, the distance between s-convex ordered random variables is investigated. Results connecting positive or negative dependence concepts and convex ordering are also presented. These results lead to approximations and bounds for the distributions of sums of positively or negatively dependent random variables. Applications and extensions of the main results pertaining to compound Poisson, normal and exponential approximation are provided as well.

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Nonparametric Estimation of Extremal Dependence Anna Kiriliouk, Johan Segers, and Michał Warchoł

Extreme Value Modeling and Risk Analysis ◽

10.1201/b19721-21 ◽

2016 ◽

pp. 373-396 ◽

Cited By ~ 1

Keyword(s):

Nonparametric Estimation ◽

Extremal Dependence

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Extremal Dependence between Temperature and Ozone over the Continental U.S.

10.5194/acp-2017-1033 ◽

2017 ◽

Author(s):

Pakawat Phalitnonkiat ◽

Wenxiu Sun ◽

Mircea D. Grigoriu ◽

Peter G. M. Hess ◽

Gennady Samorodnitsky ◽

...

Keyword(s):

Climate Model ◽

Heat Waves ◽

Strong Dependence ◽

Measurement Data ◽

The United States ◽

Value Theory ◽

Temperature Extremes ◽

Measured Temperature ◽

Extremal Dependence ◽

Year 2000

Abstract. The co-occurrence of heat waves and pollution events and the resulting high mortality rates emphasizes the importance of the co-occurrence of pollution and temperature extremes. Through the use of extreme value theory and other statistical methods ozone and temperature extremes and their joint occurrence are analyzed over the United States during the summer months (JJA) using Clean Air Status and Trends Network (CASTNET) measurement data and simulations of the present and future climate and chemistry in the Community Earth System Model (CESM1) CAM4-chem. Three simulations using CAM4-chem were analyzed: the Chemistry Climate Model Initiative (CCMI) reference experiment using specified dynamics (REFC1SD) between 1992–2010, a 25-year present-day simulation branched off the CCMI REFC2 simulation in the year 2000 and a 25-year future simulation branched off the CCMI REFC2 simulation in 2100. The latter two simulations differed in their concentration of carbon dioxide (representative of the years 2000 and 2100) but were otherwise identical. A new metric is developed to measure the joint extremal dependence of ozone and temperature by evaluating the spectral dependence of their extremes. Two regions of the U.S. give the strongest measured extreme dependence of ozone and temperature: the northeast and the southeast. The simulations do not capture the relationship between temperature and ozone over the northeast but do simulate a strong dependence of ozone on extreme temperatures over the southeast. In general, the simulations of ozone and temperature do not capture the width of the measured temperature and ozone distributions. While on average the future increase in the 90th percentile temperature and the 90th percentile ozone slightly exceed the mean increase over the continental U.S., in many regions the width of the temperature and ozone distributions decrease. The location of future increases in the tails of the ozone distribution are weakly related to those of temperature with a correlation of 0.3.

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