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Mathematical Problems in Engineering
Volume 8, Issue 1, Pages 1-13
http://dx.doi.org/10.1080/10241230211380

On stochastic inequalities and comparisons of reliability measures for weighted distributions

1Department of Mathematics and Computer Science, Georgia Southern University, Statesboro 30460-8093, GA, USA
2Department of Mathematical Sciences, The University of Memphis, USA

Received 18 December 2000

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Inequalities, relations and stochastic orderings, as well as useful ageing notions for weighted distributions are established. Also presented are preservation and stability results and comparisons for weighted and length-biased distributions. Relations for length-biased and equilibrium distributions as examples of weighted distributions are also presented.