Editing Copulas and Dependence (section)

== <span style="color: #FFFFFF;">Remembering</span> ==
* '''Copula''' — A mathematical function used to describe the "Dependence Structure" between random variables, independent of their individual distributions.
* '''Dependence''' — The "Relationship" between two variables (e.g., when X goes up, does Y go up too?).
* '''Correlation (Pearson)''' — The simplest measure of dependence: a number from -1 to +1 showing a "Linear" relationship.
* '''Sklar’s Theorem''' — The "Holy Grail" of copulas: the proof that any multi-variable distribution can be broken down into "Individual marginals" and a "Copula" that joins them.
* '''Tail Dependence''' — When two things only "Move together" during "Extreme" events (e.g., during a normal day, stocks are random; during a crash, they ALL go down).
* '''Gaussian Copula''' — A specific type of copula based on the "Normal Distribution" (Famous for its role in the 2008 Financial Crisis).
* '''Archimedean Copulas''' — A family of copulas (like Clayton or Gumbel) that are good at modeling "Asymmetric" dependence (e.g., things fail together faster than they succeed together).
* '''Marginals''' — The individual "Probability Distributions" of each variable before they are joined.
* '''Rank Correlation''' — Measuring dependence based on the "Order" of things rather than the "Values" (e.g., Kendall's Tau or Spearman's Rho).
* '''Joint Distribution''' — The final "Big Picture" of how multiple variables behave together.
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