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GENERALIZING THE LOG-MOYAL DISTRIBUTION AND REGRESSION MODELS FOR HEAVY-TAILED LOSS DATA

Published online by Cambridge University Press:  04 November 2020

Zhengxiao Li Open the ORCID record for Zhengxiao Li [Opens in a new window] ,
Jan Beirlant Open the ORCID record for Jan Beirlant [Opens in a new window]  and
Shengwang Meng Open the ORCID record for Shengwang Meng [Opens in a new window]
Zhengxiao Li
Affiliation:
School of Insurance and Economics University of International Business and EconomicsBeijing, China E-Mail: li_zhengxiao@uibe.edu.cn
Jan Beirlant
Affiliation:
Department of Mathematics, LStat and LRisk KU Leuven Leuven, Belgium and Department of Mathematical Statistics and Actuarial Science University of the Free StateBloemfontein, South Africa E-Mail: jan.beirlant@kuleuven.be
Shengwang Meng*
Affiliation:
School of Statistics Renmin University of China Beijing, China and Center for Applied Statistics Renmin University of China Beijing, China E-Mail: mengshw@ruc.edu.cn
*
E-Mail: mengshw@ruc.edu.cn
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Abstract

Catastrophic loss data are known to be heavy-tailed. Practitioners then need models that are able to capture both tail and modal parts of claim data. To this purpose, a new parametric family of loss distributions is proposed as a gamma mixture of the generalized log-Moyal distribution from Bhati and Ravi (2018), termed the generalized log-Moyal gamma (GLMGA) distribution. While the GLMGA distribution is a special case of the GB2 distribution, we show that this simpler model is effective in regression modeling of large and modal loss data. Regression modeling and applications to risk measurement are illustrated using a detailed analysis of a Chinese earthquake loss data set, comparing with the results of competing models from the literature. To this end, we discuss the probabilistic characteristics of the GLMGA and statistical estimation of the parameters through maximum likelihood. Further illustrations of the applicability of the new class of distributions are provided with the fire claim data set reported in Cummins et al. (1990) and a Norwegian fire losses data set discussed recently in Bhati and Ravi (2018).

Keywords

Generalized log-Moyal distributionparametric regression modelingfire claim data setNorwegian fire lossesChinese earthquake lossesG22
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 51 , Issue 1 , January 2021 , pp. 57 - 99
Copyright
© 2020 by Astin Bulletin. All rights reserved

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