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Measurement Procedures for the Variance of a Normal Distribution

Measurement Procedures for the Variance of a Normal Distribution Abstract Neyman prediction and measurement procedures have been discussed by E.v. Collani, M. Dumitrescu and their co-workers since 1999. These procedures offer optimal, however, computational rather intensive ways for predicting with respect to the future outcome of a random variable and measuring with respect to the actual value of a deterministic variable under the realistic condition that the range of variability of any involved variable is bounded. This paper presents an algorithm for constructing Neyman prediction and complete measurement procedures for the variance of a normal distribution (with known or unknown mean). A comparison with the traditional shortest confidence intervals is presented by means of a numerical example. The main advantages of the Neyman approach are the following: 1. the unrealistic assumption of maximal and, hence, generally unbounded range of variability is abandoned, 2. the measurements (= confidence intervals) are necessarily subsets of the bounded range of variability, and, therefore, unreasonable results are impossible, 3. the point estimation is necessarily meaningful because it is associated with a confidence interval and a specified confidence level. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Economic Quality Control de Gruyter

Measurement Procedures for the Variance of a Normal Distribution

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Publisher
de Gruyter
Copyright
Copyright © 2002 by the
ISSN
1869-6147
eISSN
1869-6147
DOI
10.1515/EQC.2002.155
Publisher site
See Article on Publisher Site

Abstract

Abstract Neyman prediction and measurement procedures have been discussed by E.v. Collani, M. Dumitrescu and their co-workers since 1999. These procedures offer optimal, however, computational rather intensive ways for predicting with respect to the future outcome of a random variable and measuring with respect to the actual value of a deterministic variable under the realistic condition that the range of variability of any involved variable is bounded. This paper presents an algorithm for constructing Neyman prediction and complete measurement procedures for the variance of a normal distribution (with known or unknown mean). A comparison with the traditional shortest confidence intervals is presented by means of a numerical example. The main advantages of the Neyman approach are the following: 1. the unrealistic assumption of maximal and, hence, generally unbounded range of variability is abandoned, 2. the measurements (= confidence intervals) are necessarily subsets of the bounded range of variability, and, therefore, unreasonable results are impossible, 3. the point estimation is necessarily meaningful because it is associated with a confidence interval and a specified confidence level.

Journal

Economic Quality Controlde Gruyter

Published: Oct 1, 2002

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