Arnold and Villasenor  obtain a series of characterizations of the exponential distribution based on random samples of size two. These results were already applied in constructing goodness-of-fit tests. Extending the techniques from , we prove some of Arnold and Villasenor’s conjectures for samples of size three. An example with simulated data is discussed.
Yanev, George, "On Arnold–Villasenor conjectures for characterizaing exponential distribution based on sample of size three" (2020). Mathematical and Statistical Sciences Faculty Publications and Presentations. 34.