Stochastic Comparisons Of Order Satistics From Weibull Distributions

The comparisons of stochastic order indicate correlativity of random variables.Korwar(2002)has shown that a convolution of gamma distribution with a common shape parameter greater than 1 is larger in likelihood ratio order when the scale parameters are more dispersed in the sense of majorization.Lihong sun(2004)has proved that when the shape parameters of gamma distribution have different value,order statistics have different stochastic order too.In this paper it will prove the conclusion as follows:with two independent random variables subjecting to different Weibull distributions with the same shape parameter,when their common parameterαis smaller than or equal to 1,the order statistics have a consistent stochastic order in the sense of majorization;However,whenαis larger than 1,it only obtain that the minimum and maximum have the reverse stochastic order.