Characterizing the distributions of three independent n-dimensional random variables, X₁, X₂, X₃, having analytic characteristic functions by the joint distribution of (X₁ + X₃, X₂ + X₃)

Paul G. Miller

Vol. 35 (1970), No. 2, 487–491

DOI: 10.2140/pjm.1970.35.487

Abstract

Kotlarski characterized the distribution of three independent real random variables X₁,X₂,X₃ having nonvanishing characteristic functions by the joint distribution of the 2-dimensional vector (X₁ + X₈,X₂ + X₃). In this paper, we shall give a generalization of Kotlarski’s result for X₁,X₂,X_a n-dimensional random variables having analytic characteristic functions which can meet the value zero.

Mathematical Subject Classification

Primary: 60.20

Milestones

Received: 18 February 1970

Published: 1 November 1970