The problem posed by exact confidence intervals (CIs) which can be either all‐inclusive or empty for a nonnegligible set of sample points is known to have no solution within CI theory. Confidence belts causing improper CIs can be modified by using margins of error from the renewed theory of errors initiated by J. W. Tukey—briefly described in the article—for which an extended Fraser's frequency interpretation is given. This approach is consistent with Kolmogorov's axiomatization of probability, in which a probability and an error measure obey the same axioms, although the connotation of the two words is different. An algorithm capable of producing a margin of error for any parameter derived from the five parameters of the bivariate normal distribution is provided. Margins of error correcting Fieller's CIs for a ratio of means are obtained, as are margins of error replacing Jolicoeur's CIs for the slope of the major axis. Margins of error using Dempster's conditioning that can correct optimal, but improper, CIs for the noncentrality parameter of a noncentral chi‐square distribution are also given.

中文翻译：

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高斯替代使用不正确的置信区间

确切的置信区间（CI）构成的问题对于CI理论无法解决，对于一组不可忽略的采样点而言，它可能是全包的，也可能是空的。可以通过使用JW Tukey提出的新错误理论中的错误余量来修改导致CI不正确的置信带，该文章已在本文中进行了简要描述，并给出了扩展的Fraser频率解释。这种方法与Kolmogorov的概率公理化方法是一致的，尽管两个词的含义不同，但概率和错误度量服从相同的公理。提供了一种能够针对从二元正态分布的五个参数导出的任何参数产生误差余量的算法。纠错Fieller'的边距 获得了均值比的CI，以及用误差率代替了Jolicoeur的主轴斜率的CI。还给出了使用Dempster条件的误差余量，该误差可以校正非中心卡方分布的非中心参数的最优CI，但不合适。