Mixed Copulas: Weighted Density, Probability, and Sampling
Summary
This class template describes a bivariate mixed copula as a weighted combination of component copulas. It calculates the mixture density, joint cumulative probability, and conditional probability by evaluating each component and summing according to its weight. The methods first clamp both uniform inputs away from the boundaries to reduce infinite or undefined values in component calculations.
The template also samples observations by randomly selecting a component according to the mixture weights, then drawing a pair from that component. A helper remaps parameters close to zero to small signed values, which can support calculations that are unstable at zero. This is implementation guidance rather than a trading strategy or empirical study: it provides no fitted parameters, validation results, or discussion of how to select copulas or weights. Its sampling implementation assumes three components, and the conditional probability method describes symmetry that may depend on the component copulas.
Key ideas
- A mixed copula combines component densities using their assigned weights.
- Joint and conditional probabilities are computed as weighted sums of component evaluations.
- Inputs are moved away from zero and one to avoid numerical boundary problems.
- Sampling chooses a component according to the mixture weights before generating a pair.
- The template does not explain how to fit or validate the component copulas or mixture weights.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.