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Moments of the poly-Cauchy density with applications in estimation

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Summary

Simple mathematical formulae for the mean and variance of a poly-Cauchy density (proportional to a product of two Cauchy densities) are derived here and then applied to obtain Bayesian estimators for the mean of a normal population and the difference between means of two normal populations. The proposed estimators are arguably superior to the traditional estimators and to the usual Bayesian estimators, and may be highly robust.

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Authors and Affiliations

  1. School of Statistics, University of Minnesota, Minnesota, USA

    James M. Dickey

  2. Department of Economics and Statistics, National University of Singapore, 10 Kent Ridge Crescent, 119260, Singapore

    Guorui Bian

Authors
  1. Guorui Bian
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  2. James M. Dickey
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Bian, G., Dickey, J.M. Moments of the poly-Cauchy density with applications in estimation. J. It. Statist. Soc. 5, 1–11 (1996). https://doi.org/10.1007/BF02589580

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  • DOI: https://doi.org/10.1007/BF02589580

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