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Exponential Approximations for Length-Biased and Weighted Residual Life Reliability Functions
by
Broderick O. Oluyede
Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30460
Coauthors: Mavis Pararai, Department of Mathematics, Indiana University of Pennsylvania, Indiana, PA 15705
The applications of weighted distributions to biased samples is well known. Applications in various areas including medicine, ecology, reliability, and branching processes can be seen in Patil and Rao (1978), Gupta and Kirmani (1990), Gupta and Keating (1985), and Oluyede (1999) to mention just a few authors. In this note, we present stochastic inequalities, bounds and stability results on the distance between length-biased reliability functions as well as weighted residual life reliability functions with monotone weight functions and their exponential counterparts in the class of distribution functions with increasing or decreasing hazard rate and mean residual life functions. Some applications are also presented.
Date received: July 3, 2007
Copyright © 2007 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # caur-35.