On the characterization of an interesting property of the arcsin distribution

Johan Henricus Bernardus Kemperman and Morris Skibinsky

Vol. 103 (1982), No. 2, 457–465

DOI: 10.2140/pjm.1982.103.457

Abstract

The property that product and sum of independent identically distributed random variables are equidistributed is characterized when the original distribution has all moments. This equidistribution property is shown to relate in a natural way to the uniform distribution on a compact group. The result proves a conjecture due to Norton.

Mathematical Subject Classification 2000

Primary: 62E10

Secondary: 22C05, 60B15

Milestones

Received: 11 November 1980

Published: 1 December 1982