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A Note on a Characterization of the Exponential Distribution Based on a Type II Censored Sample
Let $X_{(1)} \leq X_{(2)} \leq \cdots \leq X_{(n)}$ be the order statistics of a random sample of $n$ lifetimes. The total-time-on-test statistic at $X_{(i)}$ is defined by $S_{i,n} = \sum^i_{j = 1}(n - j + 1)(X_{(j)} - X_{(j - 1)}), 1 \leq i \leq n$. A type II censored sample …