# zbMATH — the first resource for mathematics

Some integration-by-parts formulas involving 2-copulas. (English) Zbl 1322.60008
Cuadras, Carles M. (ed.) et al., Distributions with given marginals and statistical modelling. Papers presented at the meeting, Barcelona, Spain, July 17–20, 2000. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-0914-3/hbk). 153-159 (2002).
Summary: We note examples of probabilistic interpretations of integrals involving 2-copulas. We then use the theory of strong convergence of copulas to justify an integration-by-parts formula involving 2-copulas,
$\int_{I^2} f(A)\,dB=\int^1_0 f(t)\,dt-\int_{I^2}-f'(A)D_1AD_2B=\int^a_0 f(t)\,dt-\int_{I_2} f'(A)D_2AD_1B$ where $$A$$ and $$B$$ are arbitrary 2-copulas and $$f$$ is continuously differentiable.
For the entire collection see [Zbl 1054.62002].

##### MSC:
 60E05 Probability distributions: general theory 62E10 Characterization and structure theory of statistical distributions 62H05 Characterization and structure theory for multivariate probability distributions; copulas
Full Text: