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Let be the order statistics of a sample of size n≥ 2 from a population with continuous distribution function F. In this paper, we obtain the distribution function F from conditional expectation
or
. where h is a real, continuous and strictly monotonic function. We give the necessary and sufficient conditions so that any real function ξ(x) is equal to
or
is equal to
. Different continuous distributions are also characterized using our results.
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