On Arnold-Villasenor Conjectures for Characterizing Exponential Distribution Based on Sample of Size Three

Arnold and Villasenor [4] 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 in [7]. Extending the techniques from [4], we prove some of Arnold and Villasenor's conjectures for samples of size three. An example with simulated data is discussed.