Journal ArticleDOI
One- and Two-Sided Tolerance Intervals for General Balanced Mixed Models and Unbalanced One-Way Random Models
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In this article, the authors developed procedures for one-and two-sided tolerance intervals for normal general linear models in which there exists a set of independent scaled chi-squared random variables.Abstract:
In this article we develop procedures for one- and two-sided tolerance intervals for normal general linear models in which there exists a set of independent scaled chi-squared random variables. The proposed procedures are based on the concept of generalized pivotal quantities and are applicable to general mixed models provided that balanced data are available. However, this study focuses on situations involving unbalanced data. Specific attention is given to the unbalanced one-way random model. It is shown that the use of generalized pivotal quantities allows the construction of the tolerance intervals of interest fairly straightforward. Some practical examples are given to illustrate the proposed procedures. Furthermore, detailed statistical simulation studies are conducted to evaluate their performance, showing that the proposed procedures can be recommended for practical use.read more
Citations
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Journal ArticleDOI
Confidence limits for stress strength reliability involving weibull models
K. Krishnamoorthy,Yin Lin +1 more
TL;DR: In this article, an interval estimation procedure based on the generalized variable (GV) approach is given when the shape parameters are unknown and arbitrary, and the coverage probabilities of the GV approach are evaluated by Monte Carlo simulation.
Journal ArticleDOI
A non-inferiority test for diagnostic accuracy based on the paired partial areas under ROC curves
TL;DR: Simulation results show that the proposed non-inferiority test not only adequately controls the size at the nominal level but also is uniformly more powerful than the non-parametric methods.
Journal ArticleDOI
Methodologies for the transfer of analytical methods: a review.
TL;DR: This paper reviews the documentation available in the scientific literature about the design of transfer studies and the required sample size and focuses on the statistical methodologies available for decision making with particular emphasis on risk management.
Journal ArticleDOI
On the exact interval estimation for the difference in paired areas under the ROC curves.
TL;DR: Simulation results demonstrate that the exact confidence interval based on the concept of GPQs provides not only sufficient probability coverage but also reasonable expected length.
Journal ArticleDOI
An overall uncertainty approach for the validation of analytical separation methods.
TL;DR: It is demonstrated here that (β, γ) tolerance intervals will provide perfect estimates of the routine uncertainty and there is no difference statistically between the uncertainties estimated by the methodology as of the validation stage with those obtained from the routine phase.
References
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Book
Matrix Algebra Useful for Statistics
TL;DR: The Matrix Algebra of Regression Analysis (MARA) as discussed by the authors is a generalization of the matrix algebra of regression analysis (MA) for linear statistical models, and it has been used in many applications in statistics.
Book ChapterDOI
Generalized Confidence Intervals
TL;DR: In this paper, a generalized version of the confidence interval is defined, and the generalized confidence interval can be applied to the problem of constructing confidence intervals for the difference in two exponential means and for variance components in mixed models.
Journal ArticleDOI
Tolerance Limits for a Normal Distribution
Abraham Wald,J. Wolfowitz +1 more
TL;DR: The problem of constructing tolerance limits for a normal universe is considered in this article, where the tolerance limits are required to be such that the probability is equal to a pre-assigned value (i.e., the probability that the tolerance limit includes at least a given proportion of the population).
Matrix Algebra Useful for Statistics
TL;DR: In this article, the matrix algebra useful for statistics that will be your best choice for better reading book is presented and five times will not spend wasted by reading this website and they will show the best book to read today.
Journal ArticleDOI
Interval Estimation for the Unbalanced Case of the One-Way Random Effects Model
TL;DR: In this paper, the interval estimation of variance components is studied for the unbalanced one-way random effects model and an easily calculated function, $W$, of the harmonic mean of the class sizes and of the sample variance of class means is found and shown to be excellently approximated by a chi-square distribution.