Copula

GROWING This note is being developed. It is readible but changes are being applied.
cards/statistics/copula.md Current Note ID: The unique ID of this note.
#statistics

Given two uniform marginals, we can apply the inverse cdf of a continuous distribution to form a new joint distribution.

Some examples in this notebook.

Uniform marginals

[[Gaussian]] Multivariate Normal Distribution Multivariate Gaussian distribution copula:

Normal, Normal

Some other examples:

  1. [[Normal]] Normal Distribution Gaussian distribution and [[Beta]] Beta Distribution Beta Distribution Interact Alpha Beta mode ((beta_mode)) median ((beta_median)) mean ((beta_mean)) ((makeGraph)) :
    Normal, Beta
  2. Gumbel and [[Beta]] Beta Distribution Beta Distribution Interact Alpha Beta mode ((beta_mode)) median ((beta_median)) mean ((beta_mean)) ((makeGraph)) :
    Gumbel, Beta
  3. [[t distribution]] t Distribution t distribution :
    t, t

Planted: by ;

References:
  1. Quant D. A Simple Introduction to Copulas. YouTube. 2021. Available: https://www.youtube.com/watch?v=WFEzkoK7tsE
  2. Wiecki T. An intuitive, visual guide to copulas — While My MCMC Gently Samples. In: While My MCMC Gently Samples [Internet]. 3 May 2018 [cited 6 Jan 2023]. Available: https://twiecki.io/blog/2018/05/03/copulas/
  3. SDV. Introduction to Copulas — Copulas 0.6.0 documentation. In: Copulas [Internet]. 2018 [cited 6 Jan 2023]. Available: https://sdv.dev/Copulas/tutorials/01_Introduction_to_Copulas.html
Similar Articles:
Jensen's Inequality
Jensen’s inequality shows that $$ f(\mathbb E(X)) \leq \mathbb E(f(X)) $$ for a concave …
Valid Confidence Sets in Multiclass and Multilabel Prediction
Ask for valid confidence: “Valid”: validate for test data, train data, or the generating …
ANOVA
analysis of variance
Schaum's Outline of Theories and Problems of Elements of Statistics I and II
The basics and all of modern statistics
Additional Double Backet Links:
Multivariate Normal Distribution
Multivariate Gaussian distribution
Normal Distribution
Gaussian distribution
Beta Distribution
Beta Distribution Interact Alpha Beta mode ((beta_mode)) median ((beta_median)) mean ((beta_mean)) …
t Distribution
t distribution

Lei Ma (2023). 'Copula', Datumorphism, 01 April. Available at: https://datumorphism.leima.is/cards/statistics/copula/.