2019/12/19 by Zhengxiao Li, Li, Zhengxiao, Jan Beirlant +3
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Applications (stat.AP) #FOS: Computer and information sciences #Insurance and Financial Risk Management #Methodology (stat.ME) #Probability and Risk Models #Statistical Distribution Estimation and Applications
paper · pdf · doi:10.48550/arxiv.1912.09560
openalex publication_date 2019/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.