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Diagonal distributions via orthogonal expansions and tests of independence. (English) Zbl 1137.62345
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). 35-42 (2002).
Summary: The Farlie-Gumbel-Morgenstern family of distributions can be extended by using Legendre polynomials. Another extension consists in using the principal dimensions of each marginal variable. These principal dimensions may improve some tests for stochastic independence.
For the entire collection see [Zbl 1054.62002].

62H25 Factor analysis and principal components; correspondence analysis
62G10 Nonparametric hypothesis testing
62E15 Exact distribution theory in statistics