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Confidence Intervals for the Scale Parameter of Exponential Family of Distributions.

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....

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Published in:American Statistician Vol. 70; no. 2; pp. 134 - 138
Main Authors: Hoshyarmanesh, Hossein, Karami, Amirhossein, Mohammadpour, Adel
Format: Article
Published: Taylor & Francis Ltd May2016
Subjects:
Confidence intervals
Exponential families (Statistics)
Sufficient statistics
Chi-square distribution
Probability density function
Online Access:View this record in EBSCOhost
Summary: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.