Copulas

Why Gaussian Copulas Look Dense at Corners but Have Zero Tail Dependence

A deep dive into the seemingly contradictory behavior of Gaussian copulas: elevated density near corners versus zero asymptotic tail dependence.

Mar 22, 2025

Understanding Gaussian Copulas and Vine Copulas

Learn about Gaussian copulas, vine copulas, and their applications in multivariate modeling with practical examples and implementation details.

Mar 22, 2025

Understanding Copulas: Separating Dependence from Marginal Distributions

Learn how copulas allow you to model dependence structures independently from marginal distributions, with detailed explanations of Gaussian and t-copulas.

Mar 22, 2025

Understanding Copulas in scDesign3: From Gaussian to Vine Copulas

Exploring how scDesign3 uses Gaussian and vine copulas to model complex dependencies between genes in single-cell RNA sequencing data.

Mar 22, 2025

Understanding Copulas and Joint Densities: From Theory to Practice

A comprehensive mathematical exploration of how copulas connect marginal distributions to create joint densities, with rigorous proofs and practical examples.

Mar 22, 2025

Understanding Clayton Copula Conditional Sampling: From Theory to Practice

Learn how the Clayton copula conditional sampling formula works, why it has that specific form, and see it in action with step-by-step numeric examples.

Mar 22, 2025

Gaussian Copulas vs Multivariate Normal

Understanding the difference between multivariate normal distributions and Gaussian copulas, with practical Python implementations.

Mar 22, 2025

Deriving Kendall's Tau from The Population Perspective (Copulas)

A complete mathematical derivation showing how Kendall's tau emerges from the copula integral formula τ = 4∫₀¹∫₀¹C(u,v)dC(u,v) - 1

Mar 22, 2025