A practical tour of the most important copula families: Gaussian, Student-t, Clayton, Gumbel, and Frank — with closed-form expressions, sampling algorithms, and visual comparisons.
You'll learn when to use each family: Clayton for lower tail dependence (e.g., financial crashes), Gumbel for upper tail dependence (e.g., joint price spikes), Student-t for symmetric heavy tails, and Frank for moderate symmetric dependence. Includes Cholesky-based sampling for elliptical copulas and K-function inversion for Archimedean copulas.
Part 7 of 14 in the Copula Short Course.
Follow along with the Jupyter notebook:
https://github.com/kkarrancsu/copula-short-course/blob/main/notebooks/7_closed_form_copulas.ipynb
---
📓 Get the full course materials: https://kirantrillium.gumroad.com/l/copula-course
Includes 14 interactive Jupyter notebooks, 4 real-world case studies, 17 exercises with solutions, and code templates.
