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Measurement Procedures for the Variance of a Normal Distribution

Author

Listed:
  • von Collani Elart

    (University of Würzburg, Sanderring 2, D-970720 Würzburg, Germany)

  • Dumitrescu Monica

    (University of Bucharest, Faculty of Mathematics, 14, Academiei St., 70109 Bucharest, Romania. mdumi@pro.math.unibuc.ro)

  • Panaite Victorina

    (University of Bucharest, Faculty of Mathematics, 14, Academiei St., 70109 Bucharest, Romania. victorina@math.math.unibuc.ro)

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.

Suggested Citation

  • von Collani Elart & Dumitrescu Monica & Panaite Victorina, 2002. "Measurement Procedures for the Variance of a Normal Distribution," Stochastics and Quality Control, De Gruyter, vol. 17(2), pages 155-176, January.
    • Handle: RePEc:bpj:ecqcon:v:17:y:2002:i:2:p:155-176:n:3
    DOI: 10.1515/EQC.2002.155
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