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Characterization through Moments of the Residual Life and Conditional Spacings

J. Navarro, M. Franco and J. M. Ruiz
Sankhyā: The Indian Journal of Statistics, Series A (1961-2002)
Vol. 60, No. 1 (Feb., 1998), pp. 36-48
Published by: Springer on behalf of the Indian Statistical Institute
Stable URL: http://www.jstor.org/stable/25051181
Page Count: 13
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Characterization through Moments of the Residual Life and Conditional Spacings
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Abstract

In this work, we give a general method to obtain a distribution function F(x) through the moment of the residual life defined by $h_{k}(x)=E((X-x)^{k}\|\ X\geq x)$, for k = 1, 2, 3,..., both in continuous and discrete cases. We also characterize F(x) through moments of conditional spacings of order statistics, which have applications in the context of the k-out-of-n systems. Moreover, we study characterizations based on relations between failure rate function and left censored moment functions, $m_{k}(x)=E(X^{k}\|\ X\geq x)$.

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