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On Characterization of Continuous Distributions by Conditional Expectation of Record Values

M. Franco and J. M. Ruiz
Sankhyā: The Indian Journal of Statistics, Series A (1961-2002)
Vol. 58, No. 1 (Feb., 1996), pp. 135-141
Published by: Springer on behalf of the Indian Statistical Institute
Stable URL: http://www.jstor.org/stable/25051089
Page Count: 7
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Abstract

Let $R_{0}$ < $R_{1}$ <... < $R_{n}$ <... be the upper record values from a population with continuous distribution function F. In this paper, we obtain the distribution function F from conditional expectation $E(h(R_{n-1})\,|\,R_{n}=x)$, where h is a real, continuous and strictly monotonic function. We give necessary and sufficient conditions so that any real function φ(x) is equal to $E(h(R_{n-1})\,|\,R_{n}=x)$. Finally, we show some counterexamples for the necessity or/and sufficiency of the assumed conditions, and different continuous distributions are also characterized using our results.

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