Two characterizations of the exponential distribution based on equalities among order statistics in a random sample of size three are proved. This proves two conjectures stated recently in Arnold and Villase˜nor .
Yanev, George and Chakraborty, Santanu, "Characterizations of Exponential Distribution Based On Sample of Size Three" (2013). Mathematical and Statistical Sciences Faculty Publications and Presentations. 41.
Pliska Studia Mathematica Bulgarica