Detailed study of 'polynomial structures in order statistics distributions'.

摘要

This thesis is based on the paper "Polynomial Structures in Order Statistics Distributions" by M. Denuit, Cl. Lefevre and Ph. Picard. We study the exact order distributions for i.i.d. random variables with arbitrary common law. The left tail distributions can be written as Abel-Gontcharoff polynomials and the right tail distributions can be expressed by Appell polynomials. The polynomial structure makes it easier to obtain closed forms and recursive methods for evaluating the distribution of frequently occurring statistics related to empirical distribution functions.