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Credibility, Hypothesis Testing and Regression Software

Published online by Cambridge University Press:  17 April 2015

Greg Taylor
Greg Taylor*
Affiliation:
Taylor Fry Consulting Actuaries, Level 8, 30 Clarence Street, Sydney NSW 2000, Australia, Centre for Actuarial Studies, Faculty of Economics and Commerce, University of Melbourne Parkville VIC 3052 Australia, Faculty of Commerce and Economics, University of New South Wales, Kensington NSW 2033, Australia, Phone: 61 2 9249 2901, Fax: 61 2 9249 2999, E-mail: greg.taylor@taylorfry.com.au
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Abstract

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It has been known since Zehnwirth (1977) that a scalar credibility coefficient is closely related to the F-statistic of an analysis of variance between and within risk clauses. The F-statistic may also be viewed as testing a certain regression structure, associated with credibility framework, against the null hypothesis of a simpler structure.

This viewpoint is extended to multi-dimensional credibility frameworks in which the credibility coefficient is a matrix (Sections 3 and 4), and to hierarchical regression credibility frameworks (Section 6). In each case the credibility coefficient is expressed in terms of the F-statistic that tests the significance of a defined regression structure against a simpler one.

Section 5 points out how the computation may be implemented in certain cases by means of regression software.

Keywords

Credibilityhierarchical credibilityhypothesis testingregression
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 37 , Issue 2 , November 2007 , pp. 517 - 535
Copyright
Copyright © ASTIN Bulletin 2007

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