Studies in the History of Probability and Statistics. XXVIII On the history of certain expansions used in mathematical statistics

Abstract

Summary This note is concerned with the history of the expansions known to probabilitists and statisticians as Charlier's A-series and Edgeworth's series. It has been pointed out (Gnedenko & Kolmogorov, 1968, Chapter 8) that both these types of expansions appear already in the mathematical work of Tchebychev, so that the names usually attached to them are historically incorrect. In the sequel we shall, however, denote them by the names familiar to statisticians. Both expansions are closely connected with the attempts to give a refinement of the classical central limit theorem in probability. The properties which are relevant in this connexion are the asymptotic properties of the sum of a small number of terms. It will be stated here that the first valid proof of these properties was given in two papers by the present author (1925, 1928).