Record values and the exponential distribution

Abstract

Let X₁, X₂, · ·· be i.i.d. and Y_k = max{X₁, X₂, · ··, X_k}. Then X_j is a record value of the sequence if Y_j > Y_j-1). Denoting record value times by L_n, n = 1, 2, ···, we prove that the independence of X_Lj − X_Li and X_Li with L_j > characterizes the exponential distribution.