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Gumbel Copula for Modeling Dependence and Generating Samples

Code Stratmill research code

Summary

This code implements a bivariate Gumbel copula for representing dependence between two uniform variables. It provides methods to generate paired samples from independent uniform inputs, calculate the copula density and cumulative distribution, and evaluate a conditional probability. The sampling procedure numerically inverts a conditional distribution using root finding, while the distribution functions are given analytically.

The class also estimates the copula parameter from Kendall’s tau using the standard relationship for this family. The parameter controls dependence, with the documented range starting at independence and extending to stronger dependence. The implementation supports externally supplied uniform pairs or random draws. It is a software description rather than a trading study: it presents no fitted market data, validation, strategy, or performance evidence. Numerical handling near the probability boundary uses a threshold, so users applying it should consider edge behavior and validate inputs and outputs for their intended use.

Key ideas

  • The Gumbel copula models dependence between two uniform variables.
  • Its cumulative distribution and density are evaluated with analytical formulas.
  • Sample pairs are generated by numerically inverting a conditional distribution.
  • The dependence parameter can be estimated from Kendall’s tau.
  • The code includes threshold handling near probability boundaries and gives no market validation.

Tags

StatisticsMachine learning

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.