Exact distribution of the max/min of two Gaussian random variables
Exact distribution of the max/min of two Gaussian random variables
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DOI：
10.1109/tvlsi.2007.912191
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发表时间：
2008-02-01
影响因子：
2.8
通讯作者：
Kotz, Samuel
中科院分区：
文献类型：
--
作者：
Nadarajah, Saralees;Kotz, Samuel
相关高斯随机变量的最大值和最小值在统计静态时间分析中自然出现。然而，最近的文献中似乎只使用了近似来研究相关高斯随机变量的最大值/最小值的分布。在本文中，我们要指出的是，统计文献早已建立了简单的表达式的确切分布的最大/最小值。我们提供了一些已知的表达式如下：概率密度函数，矩生成函数，和时刻。我们还提供了两个简单的程序计算的概率密度函数的最大值/最小值和统计静态时间分析的结果的说明。
Maximum and minimum of correlated Gaussian random variables arise naturally with respect to statistical static time analysis. It appears, however, that only approximations have been used in the recent literature to study the distribution of the max/min of correlated Gaussian random variables. In this paper, we would like to point out that the statistics literature has long established simple expressions for the exact distribution of the max/min. We provide some of the known expressions for the following: the probability density function, moment generating function, and the moments. We also provide two simple programs for computing the probability density functions of the max/min and an illustration of the results to statistical static time analysis.