Sampling Without Replacement: Approximation to the Probability Distribution

摘要

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