@article{Witkovsky_2014, title={On the Exact Two-Sided Tolerance Intervals for Univariate Normal Distribution and Linear Regression}, volume={43}, url={https://www.ajs.or.at/index.php/ajs/article/view/vol43-4-6}, DOI={10.17713/ajs.v43i4.46}, abstractNote={<p>Statistical tolerance intervals are another tool for making statistical inference on an<br />unknown population. The tolerance interval is an interval estimator based on the results<br />of a calibration experiment, which can be asserted with stated confidence level 1 ? ,<br />for example 0.95, to contain at least a specified proportion 1 ? , for example 0.99, of<br />the items in the population under consideration. Typically, the limits of the tolerance<br />intervals functionally depend on the tolerance factors. In contrast to other statistical<br />intervals commonly used for statistical inference, the tolerance intervals are used relatively<br />rarely. One reason is that the theoretical concept and computational complexity of the<br />tolerance intervals is significantly more difficult than that of the standard confidence and<br />prediction intervals.<br />In this paper we present a brief overview of the theoretical background and approaches<br />for computing the tolerance factors based on samples from one or several univariate normal<br />(Gaussian) populations, as well as the tolerance factors for the non-simultaneous<br />and simultaneous two-sided tolerance intervals for univariate linear regression. Such tolerance<br />intervals are well motivated by their applicability in the multiple-use calibration<br />problem and in construction of the calibration confidence intervals. For illustration, we<br />present examples of computing selected tolerance factors by the implemented algorithm<br />in MATLAB.</p>}, number={4}, journal={Austrian Journal of Statistics}, author={Witkovsky, Viktor}, year={2014}, month={Jun.}, pages={279–292} }