ToleranceFactorGK computes (by the Gauss-Kronod quadrature) the exact tolerance factor k for the two-sided (optionally for the one-sided) p-content and (1-alpha)-confidence tolerance interval TI = [Xmean - k * S, Xmean + k * S], where Xmean = mean(X) and S = std(X), are based on X = [X_1,...,X_n], a random sample
of size n from the distribution N(mu,sig2) with unknown mean mu and variance sig2.
ToleranceFactor computes the exact tolerance factor k for the two-sided (optionally also for the one-sided) p-content and gamma-confidence tolerance interval
TI = [Xmean - k * S, Xmean + k * S],
where Xmean = mean(X), S = std(X), X = [X_1,...,X_n] is a random sample from the distribution N(mu,sig2) with unknown mean mu and variance sig2.
The value of the tolerance factor k is determined such that the tolerance intervals with the confidence gamma cover at least the fraction p ('coverage') of the distribution N(mu,sigma^2), i.e.
Prob[ Prob( Xmean - k * S < X < Xmean + k * S ) >= p ]= gamma,
for X ~ N(mu,sig2) which is independent with Xmean and S. For more details see e.g. Krishnamoorthy and Mathew (2009).
k = ToleranceFactorGK(n,coverage,confidence)
[k,int,z,fun,options] = ToleranceFactorGK(n,coverage,confidence,m,nu,d2,options)
ISO 16269-6 (2013). Statistical interpretation of data - Part 6: Determination of statistical tolerance intervals.
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. (2013). On the exact tolerance intervals for univariate normal distribution. In: Proceedings of Computer Data Analysis & Modeling – CDAM-2013, Minsk, Belarus, September 10-14, 2013.
Institute of Mesaurement Science
Slovak Academy of Sciences
Dubravska cesta 9