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AN EM ALGORITHM FOR FITTING A NEW CLASS OF MIXED EXPONENTIAL REGRESSION MODELS WITH VARYING DISPERSION

Published online by Cambridge University Press:  08 May 2020

George Tzougas Open the ORCID record for George Tzougas [Opens in a new window]  and
Dimitris Karlis
George Tzougas*
Affiliation:
Department of Statistics, London School of Economics and Political Science, LondonWC2A 2AE, UK, E-mail: [email protected]
Dimitris Karlis
Affiliation:
Department of Statistics, Athens University of Economics and Business, Greece, E-mail: [email protected]
*
E-mail: [email protected]
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Abstract

Regression modelling involving heavy-tailed response distributions, which have heavier tails than the exponential distribution, has become increasingly popular in many insurance settings including non-life insurance. Mixed Exponential models can be considered as a natural choice for the distribution of heavy-tailed claim sizes since their tails are not exponentially bounded. This paper is concerned with introducing a general family of mixed Exponential regression models with varying dispersion which can efficiently capture the tail behaviour of losses. Our main achievement is that we present an Expectation-Maximization (EM)-type algorithm which can facilitate maximum likelihood (ML) estimation for our class of mixed Exponential models which allows for regression specifications for both the mean and dispersion parameters. Finally, a real data application based on motor insurance data is given to illustrate the versatility of the proposed EM-type algorithm.

Keywords

Mixed exponential distributionsEM algorithmregression models for the mean and dispersionparametersnon-life insuranceheavy-tailed losses
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 50 , Issue 2 , May 2020 , pp. 555 - 583
Copyright
© Astin Bulletin 2020

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