ON INEQUALITIES AND SELECTION OF EXPERIMENTS FOR LENGTH BIASED DISTRIBUTIONS

Abstract

The length biased distribution occurs naturally for some sampling plans in reliability, biometry, and survival analysis. In this note, inequalities for length biased distributions are proved for monotone hazard functions and mean residual life functions. The problem of sampling and selection of experiments from the length biased distribution as opposed to the original distribution is addressed. Certain modified cross-entropy measures are also investigated.