ABSTRACT
In this paper some characteristic properties of the uniform distribution will be considered. Let V1, V2, . . . , Vn be independent
and identically distributed random variables with distribution function FVi (x) = xi. Denote by X L(n) the nth lower record value of the sequence {X j , j = 1, 2, . . .} and by X1,n the firstorder statistics of {X1, X2, . . . , Xn}. It will be shown that the relations
X1,n d= X1,n−1Vn and X L(n) d= X L(n−1)V1
are characteristic properties of the uniform distribution.
