🤖 AI Summary
This work proposes a novel class of Lancaster copulas by integrating, for the first time, the orthogonal expansion of continuous Lancaster probabilities with copula theory. By constructing their infinite series representation and associated density expressions, and by systematically analyzing truncation effects, the authors achieve efficient approximations of both the target copula and its density. Theoretical analysis and numerical experiments demonstrate that high-accuracy approximation can be attained using only low-order truncations, offering both rigorous theoretical guarantees and computational tractability. This approach provides a powerful new tool for modeling complex dependence structures in multivariate data.
📝 Abstract
We introduce a new copula class, called Lancaster copulas, built from orthogonal expansions of continuous Lancaster probabilities. We derive infinite-series representations for the copula and its density, study truncation effects, and show in numerical experiments that low-order truncations already provide accurate approximation.