A CHARACTERIZATION OF

THE PEARSON SYSTEM OF DISTRIBUTIONS AND THE ASSOCIATED ORTHOGONAL POLYNOMIALS

V. PAPATHANASIOU

Department of Mathematics, University of Athens, Panepistemiopolis, 15784 Athens, Greece

(Received July 5, 1993; revised April 18, 1994)

Abstract. A new derivation of the classical orthogonal polynomials is given by using the w-function which appears in the variance bounds and some properties of the Pearson system of distributions. Also a characterization of the Pearson system of distributions through some conditional moments is obtained by using a result obtained by Johnson (1993) concerning this family.

Key words and phrases: Variance bounds, Pearson system, orthogonal polynomials, characterization.