TY - JOUR AU - Witkovsky, Viktor PY - 2014/06/13 Y2 - 2024/03/28 TI - On the Exact Two-Sided Tolerance Intervals for Univariate Normal Distribution and Linear Regression JF - Austrian Journal of Statistics JA - AJS VL - 43 IS - 4 SE - Articles DO - 10.17713/ajs.v43i4.46 UR - https://www.ajs.or.at/index.php/ajs/article/view/vol43-4-6 SP - 279-292 AB - <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> ER -