χ~2分布的分位数讨论及其应用

Discussion and Application of the Fractile for χ~2 Distribution

对于χ2分布利用序贯试验法中的黄金分割法,研究了其在给定α(0<α<1),满足P(a<χ2<b)=1-α的最短区间问题,并进行了计算.然后对于χ2分布参数在给定的置信度下,应用上面方法求得了此时的最短置信区间,对上法求得的最短区间与通常所用的置信区间进行比较,得到在小样本情形下优化后的结果能显著提高估计精度.

Based on the definition of Х^2 distribution fraetile, we use the golden means to compute the minimum length intervals which suit P（a 〈 Х^2 〈 b） = 1 - α, as α is from 0 to 1, and then use the same method to compute the minimum confidence interval for Х^2 distribution parameter. To compare the computed result to the normal, the minimum confidence interval can obviously improve the precision of interval estimation in the case of small sample size.