IMPROVING THE NUMERICAL TECHNIQUE FOR COMPUTING THE ACCUMULATED DISTRIBUTION OF A QUADRATIC FORM IN NORMAL VARIABLES
IMPROVING THE NUMERICAL TECHNIQUE FOR COMPUTING THE ACCUMULATED DISTRIBUTION OF A QUADRATIC FORM IN NORMAL VARIABLES
复制标题
改进计算正态变量二次形式累积分布的数值技术
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
M. King
中科院分区：
文献类型：
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作者：
Zeng;M. King
本文讨论正态变量二次型累积分布函数的数值计算方法。研究了两个新的截断界和所有已有的截断界的有效性。我们还发现，在文献中的建议进一步分裂截断误差可能会降低计算效率，最佳分裂率可以在不同的情况下是不同的。提供了一个实用的解决方案。本文还讨论了一种改进的割线算法，用于在任何给定的显着性水平上找到分布的临界值。
ABSTRACT This paper is concerned with the technique of numerically evaluating the cumulative distribution function of a quadratic form in normal variables. The efficiency of two new truncation bounds and all existing truncation bounds are investigated. We also find that the suggestion in the literature for further splitting truncation errors might reduce computational efficiency, and the optimum splitting rate could be different in different situations. A practical solution is provided. The paper also discusses a modified secant algorithm for finding the critical value of the distribution at any given significance level.