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# 關於handbook裡面3.1.3的例

 1. 關於handbook裡面3.1.3的例 ......To be more precise, we could use the chi-square distribution for the variance with k = T − 1 = 239. For the X^2(239), the 2.5% lower and 2.5% higher quantiles are q2.5% = 198.1 and q97.5% = 283.7 The exact confidence band is then sqrt(198.1/239) × 3.24% to sqrt(283.7/239) × 3.24%, or [2.949%, 3.530%] 想請問 a. q2.5%=198.1 怎麼算出來的? b. exact confidence band = sqrt(198.1/239) × 3.24% 是用哪一個公式得出? 2. A confidence interval can be constructed using the 2.5 percent lower and 2.5 percent higher cutoff values from the chi-square distribution. Define the first cutoff value as q2.5% = q[2.5%, X^2(T − 1)]. Setting this equal to the chi-square value on the right-hand side of Equation (3.6) gives the lower bound for the variance of q2.5% × s2/(T − 1). 不懂為何 q2.5% = q[2.5%, X^2(T − 1)] 帶到 Equation (3.6) 變成 q2.5% × s2/(T − 1)

 跪求解... a. q2.5%=198.1 怎麼算出來的? 可以查Chi square分布表，选择自由度为239、左尾累积概率为0.025，查出对应Chi square数值大体上为198.1。或者使用excel函数，输入=CHISQ.INV(0.025,239), 等于198.07 b.不知道你这个问题的背景，只能猜测一下：因为自由度为N的chi square变量相当于N个标准正态变量的和，所以sqrt(198.1/239) × 3.24%的构建方法实际上假定了3.24%这个数值所代表的变量应当服从一个正态分布。
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