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A method for computing tolerance intervals for a location-scale family of distributions
Computational Statistics ( IF 1.3 ) Pub Date : 2020-09-05 , DOI: 10.1007/s00180-020-01031-w
Ngan Hoang-Nguyen-Thuy , K. Krishnamoorthy

The problems of computing two-sided tolerance intervals (TIs) and equal-tailed TIs for a location-scale family of distributions are considered. The TIs are constructed using one-sided tolerance limits with the Bonferroni adjustments and then adjusting the confidence levels so that the coverage probabilities of the TIs are equal to the specified nominal confidence level. The methods are simple, exact and can be used to find TIs for all location-scale families of distributions including log-location-scale families. The computational methods are illustrated for the normal, Weibull, two-parameter Rayleigh and two-parameter exponential distributions. The computational method is applicable to find TIs based on a type II censored sample. Factors for computing two-sided TIs and equal-tailed TIs are tabulated and R functions to find tolerance factors are provided in a supplementary file. The methods are illustrated using a few practical examples.



中文翻译:

一种计算位置尺度分布族的公差区间的方法

考虑了针对位置尺度分布族计算两侧公差区间(TI)和等尾TI的问题。TI通过使用Bonferroni调整的单侧公差极限,然后调整置信度来构造,以使TI的覆盖率等于指定的标称置信度。该方法简单,准确,可用于查找所有位置范围分布族(包括对数位置范围族)的TI。说明了正态,威布尔,两参数瑞利和两参数指数分布的计算方法。该计算方法适用于基于II型删失样本查找TI。将用于计算双面TI和等尾TI的因子制成表格,并在补充文件中提供了R函数以查找公差因子。使用一些实际示例来说明这些方法。

更新日期:2020-09-07
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