Polynomial structures in rank statistics distributions

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• 作者：Claude Lef&#xe8 ; vre ; Philippe Picard
• 关键词：Rank statistics ; Kolmogorov– ; Smirnov two-sample test ; Generalized Appell and Abel– ; Gontcharoff polynomials ; Negative binomial type polynomials ; Lattice path enumeration
• 刊名：Journal of Statistical Planning and Inference
• 出版年：2011
• 出版时间：April 2011
• 年：2011
• 卷：141
• 期：4
• 页码：1380-1393
• 全文大小：268 K

文摘

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.