IMPROVING THE NUMERICAL TECHNIQUE FOR COMPUTING THE ACCUMULATED DISTRIBUTION OF A QUADRATIC FORM IN NORMAL VARIABLES
研究了计算正态变量二次型累积分布函数的数值技术，比较了新旧截断界限的效率，并提供了改进的割线算法来求临界值。
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.