On a Characterization of Uniform Distrib
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S. Dasgupta; A. Goswami; B.V. Rao
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Article
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1993
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Elsevier Science
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English
โ 392 KB
Denoting by \(X_{(1,} \leqslant X_{t 2} \leqslant \cdots \leqslant X_{(n)}\) the order statistic based on a random sample \(X_{1}, X_{2}, \ldots, X_{n}\) drawn from a distribution \(F\), it is shown that the property " \(E\left(X_{1} \mid X_{(1)}, X_{(n)}\right)=\frac{1}{2}\left(X_{(1)}+X_{(n)}\righ