Systems of probability distributions | Multivariate statistics | Actuarial science | Independence (probability theory)
In probability theory and statistics, a copula is a multivariate cumulative distribution function for which the marginal probability distribution of each variable is uniform on the interval [0, 1]. Copulas are used to describe/model the dependence (inter-correlation) between random variables. Their name, introduced by applied mathematician Abe Sklar in 1959, comes from the Latin for "link" or "tie", similar but unrelated to grammatical copulas in linguistics. Copulas have been used widely in quantitative finance to model and minimize tail risk and portfolio-optimization applications. Sklar's theorem states that any multivariate joint distribution can be written in terms of univariate marginal distribution functions and a copula which describes the dependence structure between the variables. Copulas are popular in high-dimensional statistical applications as they allow one to easily model and estimate the distribution of random vectors by estimating marginals and copulae separately. There are many parametric copula families available, which usually have parameters that control the strength of dependence. Some popular parametric copula models are outlined below. Two-dimensional copulas are known in some other areas of mathematics under the name permutons and doubly-stochastic measures. (Wikipedia).
In this video, extracted from one of my courses, I briefly speak about copulas, as tools to model multivariate random variables and distributions.
From playlist Statistical Pills
(PP 6.1) Multivariate Gaussian - definition
Introduction to the multivariate Gaussian (or multivariate Normal) distribution.
From playlist Probability Theory
(PP 6.3) Gaussian coordinates does not imply (multivariate) Gaussian
An example illustrating the fact that a vector of Gaussian random variables is not necessarily (multivariate) Gaussian.
From playlist Probability Theory
(PP 5.4) Independence, Covariance, and Correlation
(0:00) Definition of independent random variables. (5:10) Characterizations of independence. (10:54) Definition of covariance. (13:10) Definition of correlation. A playlist of the Probability Primer series is available here: http://www.youtube.com/view_play_list?p=17567A1A3F5DB5E4
From playlist Probability Theory
(PP 3.1) Random Variables - Definition and CDF
(0:00) Intuitive examples. (1:25) Definition of a random variable. (6:10) CDF of a random variable. (8:28) Distribution of a random variable. A playlist of the Probability Primer series is available here: http://www.youtube.com/view_play_list?p=17567A1A3F5DB5E4
From playlist Probability Theory
(PP 6.2) Multivariate Gaussian - examples and independence
Degenerate multivariate Gaussians. Some sketches of examples and non-examples of Gaussians. The components of a Gaussian are independent if and only if they are uncorrelated.
From playlist Probability Theory
Bruno Rémillard: Copulas based inference for discrete or mixed data
Abstract : In this talk I will introduce the multilinear empirical copula for discrete or mixed data and its asymptotic behavior will be studied. This result will then be used to construct inference procedures for multivariate data. Applications for testing independence will be presented.
From playlist Probability and Statistics
What is a conditional probability?
An introduction to the concept of conditional probabilities via a simple 2 dimensional discrete example. If you are interested in seeing more of the material, arranged into a playlist, please visit: https://www.youtube.com/playlist?list=PLFDbGp5YzjqXQ4oE4w9GVWdiokWB9gEpm For more inform
From playlist Bayesian statistics: a comprehensive course
Seminar about distortion functions and Lorenz curves in finance.
From playlist Talks and Interviews
IMS Public Lecture: Mathematics and the Financial Crisis
Paul Embrechts, Swiss Federal Institute of Technology (ETH), Zurich
From playlist Public Lectures
From playlist Contributed talks One World Symposium 2020
Pavel Krupskiy - Conditional Normal Extreme-Value Copulas.
Dr Pavel Krupskiy (University of Melbourne) presents “Conditional Normal Extreme-Value Copulas”, 14 August 2020. Seminar organised by UNSW Sydney.
From playlist Statistics Across Campuses
Pricing Credit Derivatives by Srikanth Iyer
Modern Finance and Macroeconomics: A Multidisciplinary Approach URL: http://www.icts.res.in/program/memf2015 DESCRIPTION: The financial meltdown of 2008 in the US stock markets and the subsequent protracted recession in the Western economies have accentuated the need to understand the dy
From playlist Modern Finance and Macroeconomics: A Multidisciplinary Approach
Philippe Naveau: Detecting seasonality changes in multivariate extremes from climatological time ...
Many effects of climate change seem to be reflected not in the mean temperatures, precipitation or other environmental variables, but rather in the frequency and severity of the extreme events in the distributional tails. The most serious climate-related disasters are caused by compound ev
From playlist Probability and Statistics
Statistics: Ch 4 Probability in Statistics (20 of 74) Definition of Probability
Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn the “strict” definition of experimental (empirical) and theoretical probability. Next video in this series can be seen
From playlist STATISTICS CH 4 STATISTICS IN PROBABILITY
Elena Di Bernardino: On tail dependence coefficients of transformed multivariate Archimedean ...
Abstract : This work presents the impact of a class of transformations of copulas in their upper and lower multivariate tail dependence coefficients. In particular we focus on multivariate Archimedean copulas. In the first part, we calculate multivariate transformed tail dependence coeffic
From playlist Probability and Statistics
(PP 6.6) Geometric intuition for the multivariate Gaussian (part 1)
How to visualize the effect of the eigenvalues (scaling), eigenvectors (rotation), and mean vector (shift) on the density of a multivariate Gaussian.
From playlist Probability Theory
MIT 24.900 Introduction to Linguistics, Spring 2022 Instructor: Prof. Norvin W. Richards View the complete course: https://ocw.mit.edu/courses/24-900-introduction-to-linguistics-spring-2022/ YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63BZGNOqrF2qf_yxOjuG35j This v
From playlist MIT 24.900 Introduction to Linguistics, Spring 2022