Spherical & Elliptical Distributions

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Related lectures (48)

Elliptical Distributions: Properties and Applications

Covers elliptical distributions, including properties, applications, and risk management implications.

Quantitative Risk Management: Distributions and Techniques

Covers distributions and techniques in Quantitative Risk Management for financial modeling.

Multivariate Distributions: Spherical and Elliptical

Explores spherical and elliptical distributions, normal variance mixtures, factor models, and principal component analysis.

Multivariate Statistics: Conditional Distributions

Covers conditional distributions and correlations in multivariate statistics, including partial variance and covariance, with applications to non-normal distributions.

Multivariate Statistics: Normal Distribution

Introduces multivariate statistics, covering normal distribution properties and characteristic functions.

Dependence Concepts and Copulas

Explores dependence concepts, copulas, correlation fallacies, and rank correlations in statistics.

Copulas: Properties and Applications

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

Continuous Random Variables

Explores continuous random variables, density functions, joint variables, independence, and conditional densities.

Multivariate Normal Distribution: Correlation and Covariance

Covers correlation, covariance, empirical estimates, eigenvalues, normality testing, and factor models.

Introduction to Continuous Random Variables: Probability Distributions

Introduces continuous random variables and their probability distributions, emphasizing their applications in statistics and data science.

Random Vectors & Distribution Functions

Covers random vectors, joint distribution, conditional density functions, independence, covariance, correlation, and conditional expectation.

Joint Distributions

Explores joint distributions, marginal laws, covariance, correlation, and variance properties.

Principal Component Analysis: Introduction

Introduces Principal Component Analysis, focusing on maximizing variance in linear combinations to summarize data effectively.

Copulas: Dependence Modeling

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

Continuous Random Variables

Covers continuous random variables, probability density functions, and distributions, with practical examples.

Probability and Statistics: Fundamental Theorems

Explores fundamental theorems in probability and statistics, joint probability laws, and marginal distributions.

Copulas: Properties and Applications

Covers copulas, Sklar's Theorem, meta distributions, and various dependence measures like rank correlations and coefficients of tail dependence.

Maximum Likelihood Estimation: Multivariate Statistics

Explores maximum likelihood estimation and multivariate hypothesis testing, including challenges and strategies for testing multiple hypotheses.

Sampling Theory: Statistics for Mathematicians

Covers the theory of sampling, focusing on statistics for mathematicians.

Multivariate Statistics: Wishart and Hotelling T²

Explores the Wishart distribution, properties of Wishart matrices, and the Hotelling T² distribution, including the two-sample Hotelling T² statistic.

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