Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series A, Pt. 1 ,pp. 36-48

CHARACTERIZATION THROUGH MOMENTS OF THE RESIDUAL LIFE AND CONDITIONAL SPACINGS

By

J. NAVARRO, M. FRANCO and J.M. RUIZ, University of Murcia, Spain

SUMMARY.In this work, we give a general method to obtain a distribution function F(x) through the moment of the residual life defined by hk(x)=E((X-x)k|X>= 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, mk(x)=E(Xk | X>=x).

AMS (1991) subject classification. 62E10.

Key words and phrases. Characterization, failure rate, moments of the residual life, conditional spacings, order statistics.

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