Preservation of classes of life distributions and stochastic orders under weighting

Abstract

In the paper we use a representation of weighted distributions by the Lorenz curve to obtain some results concerning their relations with life distributions. We also consider a problem of preservation of stochastic orderings under weighting. Some extensions of the results of Gupta and Keating [1986. Relations for reliability measures under length biased sampling. Scand. J. Statist. 13, 49–56] and Jain et al. [1989. Relations for reliability measures of weighted distributions. Comm. Statist. Theory Methods 18, 4393–4412] are given.