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Catastrophic loss data are known to be heavy-tailed. Practitioners then needmodels that are able to capture both tail and modal parts of claim data. Tothis purpose, a new parametric family of loss distributions is proposed as agamma mixture of the generalized log-Moyal distribution from Bhati and Ravi(2018), termed the generalized log-Moyal gamma distribution (GLMGA). We discussthe probabilistic characteristics of the GLMGA, and statistical estimation ofthe parameters through maximum likelihood. While the GLMGA distribution is aspecial case of the GB2 distribution, we show that this simpler model iseffective in regression modelling of large and modal loss data. A fire claimdata set reported in Cummins et al. (1990) and a Chinese earthquake loss dataset are used to illustrate the applicability of the proposed model.

Generalizing the log-Moyal distribution and regression models for heavy tailed loss data