Statistical interpretation of data — Part 8: Determination of prediction intervals
数据的统计解释第8部分:预测区间的确定
发布日期:
2004-09-21
ISO 16269-8:20 04规定了确定单个连续分布变量的预测区间的方法。这些是从大小为n的随机样本导出的变量的值的范围,对于该范围,可以以指定的置信度做出与来自相同群体的大小为m的进一步随机选择的样本相关的预测。
考虑了三种不同类型的总体,即标准差未知的正态分布、标准差已知的正态分布和连续但形式未知的总体。
对于这三种类型的群体中的每一种,提出了两种方法,一种用于单侧预测区间,一种用于对称双侧预测区间。在所有情况下,都可以从六个置信水平中进行选择。
针对具有未知标准偏差的正态分布和具有已知标准偏差的正态分布的总体类型提出的方法也可用于非可以转化为正态的正态分布总体。
对于具有未知标准差的正态分布和具有已知标准差的正态分布的总体类型,ISO 16269-8:20 04中提供的表格仅限于包含变量的所有其他m个采样值的预测区间。对于连续但形式未知的群体类型,表涉及包含下一m个值中的至少M-R个的预测区间,其中r取0至10或0至M-1的值,以较小的范围为准。
对于正态分布的总体,还提供了计算m个进一步观测值平均值的预测区间的程序。
ISO 16269-8:2004 specifies methods of determining prediction intervals for a single continuously distributed variable. These are ranges of values of the variable, derived from a random sample of size n, for which a prediction relating to a further randomly selected sample of size m from the same population may be made with a specified confidence.
Three different types of population are considered, namely normally distributed with unknown standard deviation, normally distributed with known standard deviation, and continuous but of unknown form.
For each of these three types of population, two methods are presented, one for one-sided prediction intervals and one for symmetric two-sided prediction intervals. In all cases, there is a choice from among six confidence levels.
The methods presented for types of population that are normally distributed with unknown standard deviation and normally distributed with known standard deviation may also be used for non-normally distributed populations that can be transformed to normality.
For types of population that are normally distributed with unknown standard deviation and normally distributed with known standard deviation, the tables presented in ISO 16269-8:2004 are restricted to prediction intervals containing all the further m sampled values of the variable. For types of population that are continuous but of unknown form, the tables relate to prediction intervals that contain at least m - r of the next m values, where r takes values from 0 to 10 or 0 to m - 1, whichever range is smaller.
For normally distributed populations, a procedure is also provided for calculating prediction intervals for the mean of m further observations.