A Confidence Interval for Treatment Component-of-variance with Applications to Differences in Means of Two Exponential Distributions


There is no exact small sample solution for setting confidence intervals for the treatment component in one factor components-of-varience problem, or for the problem of setting confidence intervals for the difference in means of two exponential distributions. A large number of approximate methods have been proposed for the components-of-varience problem. In a published study of nine of these methods, two have shown promise. The properties of these two as well as a third method, proposed by the authors, are investigated and shown to perform surprisingly well in the components-of-varience setting. The problem concerning difference of two exponential means is mathematically similar to the components-of-varience problem except that the parameter about which a confidence interval is to be built may take negative values. One may also wish to require a symmetry in the method so that the solution does not depend on the order in which the two samples are labelled.Adaptations of the above mentioned methods to the exponential means problem are given. It is shown, by a Monte-Carlo study, that two of the methods perform quite well for the exponential problem.


Mathematics and Statistics

Keywords and Phrases

interval estimation; one factor random effects model; two sample exponential problem

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Document Type

Article - Journal

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© 2007 Taylor & Francis, All rights reserved.

Publication Date

01 Jan 2007