耐受性Factor计算双面的精确公差因子k(可选地用于单侧)p含量和(1-alpha) - 离子公差间隔ti = [xmean - k * s,xmean + k * s],在哪里Xmean =均值(x),s = std(x),x = [x_1,...,x_n]是从分布n(mu,sig2)的随机样本,具有未知的平均mu和方差sig2。
确定公差因子K,使得具有置信度(1-α)的公差间隔至少覆盖分布N(mu,Sigma ^ 2)的馏分P('覆盖'),即
Prob[ Prob( Xmean - k * S < X < Xmean + k * S ) >= p ]= 1-alpha, for X ~ N(mu,sig2) which is independent with Xmean and S.
SYNTAX:
k = ToleranceFactor(n,coverage,confidence)
k = ToleranceFactor(n,coverage,confidence,m,nu,d2,options)
k =容忍物质活动器(n,coverage,confence,[],[],[],选项)
参考文献:
Krishnamoorthy K, Mathew T. (2009). Statistical Tolerance Regions: Theory, Applications, and Computation. John Wiley & Sons, Inc., Hoboken, New Jersey. ISBN: 978-0-470-38026-0, 512 pages.
Witkovsky V. On the exact two-sided tolerance intervals for univariate normal distribution and linear regression. Austrian Journal of Statistics 43(4), 2014, 279-92. http:// ajs.data-analysis.at/index.php/ajs/article/viewFile/vol43-4-6/35
ISO 16269-6:2013: Statistical interpretation of data - Part 6: Determination of statistical tolerance intervals.https://www.iso.org/standard/57191.html.
Viktor Witkovsky.(2020).宽容性反应器(//www.tatmou.com/matlabcentral/fileexchange/24135-tolerancefactor), MATLAB Central File Exchange. Retrieved.
@Pete: The presented result of ToleranceFactorGK(30,.95,.95) = 2.5549 (2.554892813277693) is in good agreement with the factor K = 2.555 from Table B2 in Krishnamoorthy & Mathew (2009, p. 368), as well as with the numerical output of R package tolerance:
K.factor(30, P = 0.95, side = 2, method = "EXACT", m = 50) = 2.554893.
The problem with many other sources is that they are based either on approximations or on not well documented method/algorithm.
Prima facie, this looks well written and well documented. It seems to give results that are highly correlated with, but slightly from, various websites (all of which agree with each other). For example:
>> ToleranceFactorGK(30,.95,.95)
ans = 2.5549
Whereas the following all give it as 2.549
-http://statpages.org/tolintvl.html
-http://www.astm.org/standardization-news/data-points/statistical-intervals-part-3-nd11.html
-http://www.webapps.cee.vt.edu/ewr/environmental/teach/smprimer/intervals/interval.html
The difference is small though, particularly at large N, and any fault may lie with the websites rather than this function (unsure). Any explanation for this difference would be much appreciated.
Thanks for posting