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). 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. Regression modelling 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).
R Markdown documents are fully reproducible. Anyone who runs the codes in R studio should read the data from eqdata.csv
- ynew_: Economic Losses (adjusted) - y_: Economic Losses (original) - death_: the number of deaths from an earthquake event - inj_: the number of injures from an earthquake event - hour_, min, time: the exact time of an first earthquake event - magnitude_, intensity : the magnitude and maximum intensity of an earthquake event
The R code that was used to analyse the data can be obtained below: