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Simple Estimation Intervals for Poisson, Exponential, and Inverse Gaussian Means Obtained by Symmetrizing the Likelihood Function

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  • Eloísa Díaz-Francés

Abstract

Likelihood intervals for the Poisson, exponential, and inverse Gaussian means that have simple analytically closed expressions and good coverage frequencies for any sample size are given here explicitly. Their simplicity is striking and they should be more broadly used in applications everywhere. Their soundness is due to three statistical properties that these three distributions share as well as the fact that for all of them there exists a simple power reparameterization that symmetrizes the corresponding likelihood function. As a consequence, asymptotic maximum likelihood results are applicable even for samples of size one. Likelihood intervals of the new parameter may be easily transformed back to the original parameter of interest, the mean, by the invariance property of the likelihood function. Practical examples are given to illustrate the proposed inferential procedures.

Suggested Citation

  • Eloísa Díaz-Francés, 2016. "Simple Estimation Intervals for Poisson, Exponential, and Inverse Gaussian Means Obtained by Symmetrizing the Likelihood Function," The American Statistician, Taylor & Francis Journals, vol. 70(2), pages 171-180, May.
    • Handle: RePEc:taf:amstat:v:70:y:2016:i:2:p:171-180
    DOI: 10.1080/00031305.2015.1123187
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    References listed on IDEAS

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    1. Boyles, Russell A., 2008. "The Role of Likelihood in Interval Estimation," The American Statistician, American Statistical Association, vol. 62, pages 22-26, February.
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