【Publication Time】2021.01.15

【Lead Author】Li, Zhengxiao

【Corresponding Author】孟生旺

【Journal】 ASTIN BULLETIN

【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 distribution (GLMGA). We discuss the probabilistic characteristics of the GLMGA, and statistical estimation of the parameters through maximum likelihood. While the GLMGA distribution is a special case of the GB2 distribution, we show that this simpler model is effective in regression modelling of large and modal loss data. A fire claim data set reported in Cummins et al. (1990) and a Chinese earthquake loss data set are used to illustrate the applicability of the proposed model.

【Keywords】

Generalized log-Moyal distribution; parametric regression modeling; fire claim data set; Norwegian fire losses; Chinese earthquake losses; G22