关于Gamma分布的秩序统计量的随机比较
Stochastic Comparisons of Order Statistics from Gamma Distributions
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摘要: 对于独立不同分布的两个Gamma样本,当它们相同的形状参数大于或等于1时,最近Korwar(2002)证明了,当它们的尺度参数满足优化序时,样本的卷积就满足似然比序.本文我们证明了,当Gamma分布的形状参数小于1时,样本的对应秩序统计量之间存在一致的一般随机序;然而当形状参数大于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.Abstract: Recently, Korwar has shown that a convolution of gamma distributions 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. In this paper, we show that the order statistic of gamma distribution is larger in stochastic order when the shape parameter is smaller than or equal to 1 and the scale parameters are more dispersed in the sense of majorization. However, when the shape parameter is larger than 1, we only obtain that the minima is larger and maxima is smaller in stochastic order.