Sankhya: The Indian Journal of Statistics

1999, Volume 61, Series A, Pt. 1 ,pp. 148--151

SELECTING THE t A CHARACTERIZATION OF THE UNIFORM DISTRIBUTION VIA MOMENTS OF N-FOLD CONVOLUTION MODULO ONE

By

YUNSHYONG CHOW Institute of Mathematics, Taipei
and
SU-YUN HUANG Institute of Statistical Science, Taipei

SUMMARY. In a remarkable paper by Lin (1988), the uniform distribution U(0,1) is neatly characterized by two moment conditions: E,max (X1,X2)=2/3, and EX12=1/3. In this note, we characterize U(0,1) via moments of n-fold convolution modulo one.

AMS (1991) subject classification.62E15, 60E10.

Key words and phrases. Characterization, uniform distribution, convolution modulo one, Bernoulli polynomials, multiresolution analysis.

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