基于Weibull分布的次序统计量的随机比较

随机序的比较是对随机变量之间相关关系的一种刻画.在文中将证明:对于独立不同分布的两个Weibull分布样本,当它们共同的形状参数α不超过1时,样本对应的次序统计量之间存在一致的一般随机序,然而,当α大于1时,样本对应的极大值和极小值统计量有着相反的一般随机序.

Stochastic comparisons of order statistics from Weibull distributions

The comparisons of stochastic order indicate correlativity of random variables. 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 parameter a is smaller than or equal to 1, the order statistics have a consistent stochastic order in the sense of majorization; However, when a is larger than 1, it obtains that the minimum and maximum have the reverse stochastic order.