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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Tolerance interval ： ウィキペディア英語版 Tolerance interval A tolerance interval is a statistical interval within which, with some confidence level, a specified proportion of a sampled population falls. "More specifically, a 100×p%/100×(1−α) tolerance interval provides limits within which at least a certain proportion (p) of the population falls with a given level of confidence (1−α)."〔D. S. Young (2010), Book Reviews: "Statistical Tolerance Regions: Theory, Applications, and Computation", TECHNOMETRICS, FEBRUARY 2010, VOL. 52, NO. 1, pp.143-144.〕 "A (p, 1−α) tolerance interval (TI) based on a sample is constructed so that it would include at least a proportion p of the sampled population with confidence 1−α; such a TI is usually referred to as p-content − (1−α) coverage TI."〔Krishnamoorthy, K. and Lian, Xiaodong(2011) 'Closed-form approximate tolerance intervals for some general linear models and comparison studies', Journal of Statistical Computation and Simulation,, First published on: 13 June 2011 〕 "A (p, 1−α) upper tolerance limit (TL) is simply an 1−α upper confidence limit for the 100 p percentile of the population."〔 A tolerance interval can be seen as a statistical version of a probability interval. "In the parameters-known case, a 95% tolerance interval and a 95% prediction interval are the same." If we knew a population's exact parameters, we would be able to compute a range within which a certain proportion of the population falls. For example, if we know a population is normally distributed with mean $\backslash mu$ and standard deviation $\backslash sigma$, then the interval $\backslash mu\; \backslash pm\; 1.96\backslash sigma$ includes 95% of the population (1.96 is the z-score for 95% coverage of a normally distributed population). However, if we have only a sample from the population, we know only the sample mean $\backslash hat$ and sample standard deviation $\backslash hat$, which are only estimates of the true parameters. In that case, $\backslash hat\; \backslash pm\; 1.96\backslash hat$ will not necessarily include 95% of the population, due to variance in these estimates. A tolerance interval bounds this variance by introducing a confidence level $\backslash gamma$, which is the confidence with which this interval actually includes the specified proportion of the population. For a normally distributed population, a z-score can be transformed into a "''k'' factor" or tolerance factor〔(【引用サイトリンク】publisher= ISO 16269-6 )〕 for a given $\backslash gamma$ via lookup tables or several approximation formulas. "As the degrees of freedom approach infinity, the prediction and tolerance intervals become equal." ==Formulas== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Tolerance interval」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.