Distributional relations of the form Y d= X +T where X, Y, and T are record values or order statistics and the random translator T is independent from X are considered. Characterizations of the exponential distribution when the ordered random variables are non-neighboring are proved. Corollaries for Pareto and power function distributions are also derived.
Ahsanullah, M.; Shah, Imtiyaz A.; and Yanev, George, "On Characterizations of Exponential Distribution through Order Statistics and Record Values with Random Shifts" (2013). Mathematical and Statistical Sciences Faculty Publications and Presentations. 42.
Journal of Statistics Applications & Probability