IJPAM: Volume 49, No. 3 (2008)

ON THE CONNECTION BETWEEN CHARACTERIZATION
THEOREMS OF POLYA AND SKITOVICH-DARMOIS

N. Vakhania
Institute of Computational Mathematics
8, Acury Str., Tbilisi, 0193, GEORGIA
e-mail: nvakhania@yahoo.com


Abstract.The two basic theorems of characterization of Gaussian (normal) distributions are those of Polya's and Skitovich-Darmais'. The first of this two can be proved by the elementary methods based on the Levy Continuity Theorem, while the second one uses non-elementary and non-statistical tools from the theory of analytic functions. We give an elementary proof of Sticovih-Darmais' Theorem for the case of two random variables in each of the two linear forms. The proof is based on the reduction of Sticovih-Darmais' Theorem to Polya's Theorem.

Received: August 14, 2008

AMS Subject Classification: 60E15, 60E07

Key Words and Phrases: characterization of Gaussian distribution, Sticovih-Darmais' Theorem, Polya's Theorem

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 49
Issue: 3