SAMPLING WITHOUT REPLACEMENT - APPROXIMATION TO THE PROBABILITY-DISTRIBUTION

Abstract

AbstractLet P be the probability distribution of a sample without replacement of size n from a finite population represented by the set N={1,2,…N}. For each r=0, 1, …, an approximation Pr is described such that the uniform norm ‖P − Pr‖ is of order (n2/N)r+1 if n2/N→0. The approximation Pr is a linear combination of uniform probability product-measures concentrated on certain subspaces of the sample space Nn.