Confidence Intervals for the Scale Parameter of Exponential Family of Distributions

Hossein Hoshyarmanesh, Amirhossein Karami and Adel Mohammadpour

The American Statistician, 2016, vol. 70, issue 2, 134-137

Abstract: This article presents a unified approach for computing nonequal tail optimal confidence intervals (CIs) for the scale parameter of the exponential family of distributions. We prove that there exists a pivotal quantity, as a function of a complete sufficient statistic, with a chi-square distribution. Using the similarity between equations of shortest, unbiased, and highest density CIs, all equations are reduced into a system of two equations that can be solved via a straightforward algorithm.

Date: 2016
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DOI: 10.1080/00031305.2015.1123184

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