Ⅰ型极值分布随机变量的随机比较(英文)

Stochastic Comparisons of Random Variables from Extreme Value Distribution of Type Ⅰ

研究了两个相互独立的Ⅰ型极大值分布随机变量间的随机序,似然比序,危险率序及凸序之间的相互关系,给出了两个相互独立但不同分布的随机变量满足各种随机序时其分布所含参数间的相应关系.文中也给出了两组相互独立但不同分布的随机变量极值间在一般随机序下的大小关系.

Two independent random variables that come from extreme value distribution of type Ⅰ are compared in the usual stochastic order, likelihood ratio order, hazard ratio order and convex order. The relationship between the parameters of the cumulative distribution functions is derived when the random variable have the orders above. We also give the relationship of the order statistics that come from two groups of independent random variables.