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Second Order Bayes Prediction of Functionals of Exponential Dispersion Distributions and an Application to the Prediction of the Tails

Published online by Cambridge University Press:  17 April 2015

Zinoviy Landsman
Zinoviy Landsman*
Affiliation:
Department of Statistics, University of Haifa, Mount Carmel, Haifa 31905, Israel. E-mail: landsman@stat.haifa.ac.il
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Abstract

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Second order Bayes estimators, being the main tool in second order optimal statistical theory, provide a natural basis for a new approach to the problem of the prediction of functions of expectation functional for members of an exponential dispersion family. A general formula, providing such prediction up to the term of the order 1/n, is suggested and the application to the problem of the prediction of the tail of distributions is demonstrated. The results are illustrated with normal and gamma claim sizes. The numerical experiment demonstrates the high effectiveness of the approach even for small sample sizes.

Keywords

Second order Bayes estimatorpredictive tailpredictive meancredibility formulalower truncated meanvariance functions
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 34 , Issue 2 , November 2004 , pp. 285 - 298
Copyright
Copyright © ASTIN Bulletin 2004

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