We prove that the exponential distribution is the only one which satisfies a regression identity. This identity involves conditional expectation of the sample mean of record values given two record values outside of the sample.
Yanev, George P. 2011. “Characterizations of Exponential Distribution Via Conditional Expectations of Record Values.” Pliska Studia Mathematica Bulgarica 20 (January): 233–42.
Pliska Studia Mathematica Bulgarica