Lecture

Copulas and Margins: Extremal Dependence in Statistics

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Description

This lecture explores copulas and margins in statistics, focusing on extremal dependence. It covers topics such as the choice of marginal distributions for copulas, logistic copulas, Kendall's tau for measuring dependence, extremal correlation, and the multivariate Student t distribution. The lecture also delves into the concept of extremal correlation, asymptotic dependence, and the strength of dependence for different distributions.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Official source

Related concepts (29)

Correlation

In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are linearly related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve.

Long-range dependence

Long-range dependence (LRD), also called long memory or long-range persistence, is a phenomenon that may arise in the analysis of spatial or time series data. It relates to the rate of decay of statistical dependence of two points with increasing time interval or spatial distance between the points. A phenomenon is usually considered to have long-range dependence if the dependence decays more slowly than an exponential decay, typically a power-like decay. LRD is often related to self-similar processes or fields.

Physical dependence

Physical dependence is a physical condition caused by chronic use of a tolerance-forming drug, in which abrupt or gradual drug withdrawal causes unpleasant physical symptoms. Physical dependence can develop from low-dose therapeutic use of certain medications such as benzodiazepines, opioids, antiepileptics and antidepressants, as well as the recreational misuse of drugs such as alcohol, opioids and benzodiazepines. The higher the dose used, the greater the duration of use, and the earlier age use began are predictive of worsened physical dependence and thus more severe withdrawal syndromes.

Substance dependence

Substance dependence, also known as drug dependence, is a biopsychological situation whereby an individual's functionality is dependent on the necessitated re-consumption of a psychoactive substance because of an adaptive state that has developed within the individual from psychoactive substance consumption that results in the experience of withdrawal and that necessitates the re-consumption of the drug. A drug addiction, a distinct concept from substance dependence, is defined as compulsive, out-of-control drug use, despite negative consequences.

Independence (probability theory)

Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes. Two events are independent, statistically independent, or stochastically independent if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds. Similarly, two random variables are independent if the realization of one does not affect the probability distribution of the other.

Related lectures (64)

Copulas: Dependence Modeling

Covers copulas, Sklar's Theorem, types of copulas, and simulation of copulas for risk management.

Copulas and Tail Dependence

Explores copulas, rank correlations, and tail dependence measures in risk management.

Copulas: Properties and Applications

Explores copulas in multivariate statistics, covering properties, fallacies, and applications in modeling dependence structures.

Probability Distributions in Environmental Studies

Explores probability distributions for random variables in air pollution and climate change studies, covering descriptive and inferential statistics.