基本介紹
- 中文名:容許區間
- 外文名:tolerance interval
- 所屬學科:數學(統計學)
- 相關概念:可信度、標準差,均值等
定義,參考值範圍,
定義
(1)
為雙側界值時:按標準正態變數值的分布規律
,有




式(1)表示正態變數值
以
的機率落在式(2)的範圍內。式(2)為正態變數值
的雙側
容許區間計算公式。








(2)
為單側界值時:按標準正態變數值的分布規律
,有














參考值範圍






下面用常態分配法求參考值範圍。
常態分配法適用於正態或近似常態分配資料。
(1)正態變數
的雙側
參考值範圍計算公式:





(2)正態變數
的單側
參考值範圍為:





式(5)和式(6)中的
和
均由大樣本算得。常用
界值見表1。



![]() | 單側 | 雙側 |
0.01 | 2.326 | 2.576 |
0.05 | 1.645 | 1.960 |
0.10 | 1.282 | 1.645 |
0.20 | 0.842 | 1.282 |
為方便起見,下面列出常用求常態分配資料95%參考值範圍的方法及計算公式:
雙側95%的界限值為:
;

單側95%的上限值為:
;

單側95%的下限值為:
。
