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September, 1973 A Note on Two-Sided Confidence Intervals for Linear Functions of the Normal Mean and Variance
C. E. Land, B. R. Johnson, V. M. Joshi
Ann. Statist. 1(5): 940-943 (September, 1973). DOI: 10.1214/aos/1176342514

Abstract

The confidence sets for linear functions $\mu + \lambda\sigma^2$ of the mean $\mu$ and variance $\sigma^2$ of a normal distribution, defined in terms of the uniformly most powerful unbiased level $\alpha$ tests of hypotheses of form $H_0(\lambda, m): \mu + \lambda\sigma^2 = m$ against the two-sided alternative $H_1(\lambda, m): \mu + \lambda\sigma^2 \neq m$ for $-\infty < m < \infty$, for fixed $\alpha$ and $\lambda$, are shown to be intervals if the number of degrees of freedom for estimating $\sigma^2$ is $\geqq 2$.

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C. E. Land. B. R. Johnson. V. M. Joshi. "A Note on Two-Sided Confidence Intervals for Linear Functions of the Normal Mean and Variance." Ann. Statist. 1 (5) 940 - 943, September, 1973. https://doi.org/10.1214/aos/1176342514

Information

Published: September, 1973
First available in Project Euclid: 12 April 2007

zbMATH: 0273.62021
MathSciNet: MR345294
Digital Object Identifier: 10.1214/aos/1176342514

Subjects:
Primary: 62F25
Secondary: 62F05

Keywords: confidence intervals , linear functions of mean and variance , Lognormal distribution , normal distribution

Rights: Copyright © 1973 Institute of Mathematical Statistics

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Vol.1 • No. 5 • September, 1973
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