Characterizations based on record values and order statistics

Consider a sequence of independent and identically distributed random variables {Xi,i⩾1}{Xi,i⩾1} with a common absolutely continuous distribution function F  . Let X1:n⩽X2:n⩽⋯⩽Xn:nX1:n⩽X2:n⩽⋯⩽Xn:n be the order statistics of {X1,X2,…,Xn}{X1,X2,…,Xn} and {Yl,l⩾1}{Yl,l⩾1} be the sequence of record values generated by {Xi,i⩾1}{Xi,i⩾1}. In this work, the conditional distribution of YlYl given Xn:nXn:n is established. Some characterizations of F   based on record values and Xn:nXn:n are then given.