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Polynomial structures in rank statistics distributions
Authors:Claude Lefèvre  Philippe Picard
Affiliation:1. Université Libre de Bruxelles, Département de Mathématique, Campus de la Plaine, C.P. 210, B-1050 Bruxelles, Belgium;2. Université de Lyon, Institut de Science Financière et d’Assurances, 50 Avenue Tony Garnier, F-69007 Lyon, France
Abstract:This paper deals with the classical problem of how to evaluate the joint rank statistics distributions for two independent i.i.d. samples from a common continuous distribution. It is pointed that these distributions rely on an underlying polynomial structure of negative binomial type. That property is exploited to obtain, in a systematic and unified way, closed forms and simple recursions, some well established, for computing the joint tail and rectangular probabilities of interest.
Keywords:
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