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 (X_{1},X_{2})=2/3, and
EX_{1}^{2}=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.