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Confidence Intervals for the Scale Parameter of Exponential Family of Distributions

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  • Hossein Hoshyarmanesh
  • Amirhossein Karami
  • Adel Mohammadpour

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.

Suggested Citation

  • Hossein Hoshyarmanesh & Amirhossein Karami & Adel Mohammadpour, 2016. "Confidence Intervals for the Scale Parameter of Exponential Family of Distributions," The American Statistician, Taylor & Francis Journals, vol. 70(2), pages 134-137, May.
    • Handle: RePEc:taf:amstat:v:70:y:2016:i:2:p:134-137
    DOI: 10.1080/00031305.2015.1123184
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