关于Weibull分布的随机序

On Comparisions of Stochastic Order for Weibull Distribution

主要讨论了服从Weibull分布的2个随机向量X与Y的秩序统计量的随机序的比较,其中X与Y服从形状参数β一样而尺度参数分别为λ与μ,λ控制μ.当形状参数β小于等于1时,X的秩序统计量在一般随机序下一致大于Y的秩序统计量,当形状参数β大于1时,在一般随机序下X的极小值小于Y的极小值,而X的极大值大于Y的极大值.

In this paper, we showed that the stochastic comparisions of two stochastic vectors X and Y which are from weibull distribution with a common shape parameter β and scale parameters λ and μ respectively, is majorized by λ . The order statistics of X is larger than the order statistics of Y in stochastic order when shape parameter is smaller than or equal to 1 . However, the minima of X is smaller than the minima of Yand the maxima of X is larger than the maxima of Y in stochastic order when shape parameter is larger than 1.