Journal of Inequalities and Applications
Volume 5 (2000), Issue 5, Pages 447-466

On some length biased inequalities for reliability measures

Broderick O. Oluyede

Department of Statistics, University of Georgia, Athens 30602-1952, GA, USA

Received 31 May 1999; Revised 16 August 1999

Copyright © 2000 Broderick O. Oluyede. 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.


In this note, inequalities for length biased and the original residual life function and equilibrium distribution function with monotone hazard rate and mean residual life functions are derived. We also obtain estimates of the length biased probability density function and hazard function under random censoring. Finally, the Bayesian exponential reliability estimate under length biased sampling using a conjugate prior for the scale parameter is given.