  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.
