On the moment distributions of moments in the case of samples drawn from a limited universe

Abstract

(1) The problem of calculating the moment distributions of samples drawn en bloc from a limited universe may be attacked in many ways. It always reduces to the calculation of the values of symmetric functions. For theoretical purposes the complete solution of the problem has been given by Tschuprow. He has obtained general formulæ by means of which the results can be written down step by step and general conclusions as to the nature of the moment distributions can be deduced from Tschuprow’s formulæ. He points out, however, that the final results become very complex in the case of moments of moderately high orders.