On a property of absolute moments. (English. Russian original) Zbl 0627.60019

Braverman, M. Sh.

Theory Probab. Math. Stat. 34, 29-37 (1987); translation from Teor. Veroyatn. Mat. Stat. 34, 27-36 (1986).

Consider two pairs (X,Z) and (Y,U) of independent symmetric random variables where Z and U are identically distributed and nonzero. Let p be a fixed positive number \(p\neq 2m\) \((m=1,2,...)\). This article establishes a result that if the p-th absolute moments of \(Y+tU\) and \(X+tZ\) are equal for all real t then X and Y are equidistributed. Characteristic functions and Mellin transforms are used in establishing the result.

Reviewer: A.M.Mathai

MSC:

60E05	Probability distributions: general theory
60E10	Characteristic functions; other transforms
44A60	Moment problems

Keywords:

equidistributed random variables; absolute moments; symmetric random variables; Characteristic functions; Mellin transforms