Characterizations of distributions via order statistics with random   exponential shifts
  A class of probability distributions is characterized via equalities in law between two order statistics shifted by independent exponential variables. An explicit formula for the quintile function of the identified family of distributions is obtained. The results extend some known characterizations of exponential and logistic distributions. 
M. Ahsanullah, V.B. Nevzorov and George P. Yanev
math.PR math.ST stat.TH