Moments of the poly-Cauchy density with applications in estimation |
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| Authors: | Guorui Bian James M Dickey |
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| Institution: | (1) School of Statistics, University of Minnesota, Minnesota, USA;(2) Department of Economics and Statistics, National University of Singapore, 10 Kent Ridge Crescent, 119260, Singapore |
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| Abstract: | 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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| Keywords: | Independent prior Normal populations Poly-Cauchy distribution Poly-t distribution Posterior mean |
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