翻訳と辞書 Words near each other ・ Pivot point ・ Pivot point (technical analysis) ・ Pivot shear ・ Pivot table ・ Pivot turn ・ Pivot turn (skiing) ・ Pivot Wireless ・ Pivot-shift test ・ Pivotal ・ Pivotal (horse) ・ Pivotal altitude ・ Pivotal CRM ・ Pivotal Games ・ Pivotal Greenplum Database ・ Pivotal Labs ・ Pivotal quantity ・ Pivotal response therapy ・ Pivotal Rockordings ・ Pivotal Software ・ Pivotal trial ・ PivotLink ・ PivotNorth Capital ・ PivotPoint Technology Corporation ・ PivotX ・ Pivovar Eggenberg ・ Pivovar Kocour Varnsdorf ・ Pivovara Ličanka ・ Pivoxazepam ・ Pivín ・ PIW Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Pivotal quantity ： ウィキペディア英語版 Pivotal quantity In statistics, a pivotal quantity or pivot is a function of observations and unobservable parameters whose probability distribution does not depend on the unknown parameters 〔Shao, J.: ''Mathematical Statistics'', Springer, New York, 2003, ISBN 978-0-387-95382-3 (Section 7.1)〕 (also referred to as nuisance parameters). Note that a pivot quantity need not be a statistic—the function and its ''value'' can depend on the parameters of the model, but its ''distribution'' must not. If it is a statistic, then it is known as an ''ancillary statistic.'' More formally,〔Morris H. DeGroot, Mark J. Schervish: ''Probability and Statistics'' (4th Edition), Pearson, 2011 (page 489)〕 let $X\; =\; (X\_1,X\_2,\backslash ldots,X\_n)$ be a random sample from a distribution that depends on a parameter (or vector of parameters) $\backslash theta$. Let $g(X,\backslash theta)$ be a random variable whose distribution is the same for all $\backslash theta$. Then $g$ is called a ''pivotal quantity'' (or simply a ''pivot''). Pivotal quantities are commonly used for normalization to allow data from different data sets to be compared. It is relatively easy to construct pivots for location and scale parameters: for the former we form differences so that location cancels, for the latter ratios so that scale cancels. Pivotal quantities are fundamental to the construction of test statistics, as they allow the statistic to not depend on parameters – for example, Student's t-statistic is for a normal distribution with unknown variance (and mean). They also provide one method of constructing confidence intervals, and the use of pivotal quantities improves performance of the bootstrap. In the form of ancillary statistics, they can be used to construct frequentist prediction intervals (predictive confidence intervals). == Examples == 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「Pivotal quantity」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.