Stochastic Orders of Weighted Distributions

In this paper, we make use of a representation of weighted distributions given by Błażej (8002) [Preservation of classes of life distributions under weighting with a general weightfunction, Stat. and Prob. Lett., 82, 6004-6043], for the preservation of several weak stochastic orders under weighting. Using the previous results of Misra et al. (8002), we also obtain a preservation result of some ageing classes under weighting [Preservation of some agingproperties and stochastic orders by weighted distributions. Commun. Stat. Theory Methods, 68, 488-466]. By considering order statistics, record values, proportional hazards and proportional reversed hazards models as weighted distributions, we show that the result givenfor preservation of stochastic orders by weighting, is well motivated. One more situation where the result, is applicable, is comparisons of scale-shape families based on stochastic orders.

کلیدواژه ها:

Weigthed distributions ، Preservation ، Partial order ، IFR ، DFRA ، ILR Size biased distribution