Modelling insurance losses using contaminated generalised beta type-II distribution

The four-parameter distribution family, the generalised beta type-II (GB2), also known as the transformed beta distribution, has been proposed for modelling insurance losses. As special cases, this family nests many distributions with light and heavy tails, including the lognormal, gamma, Weibull, Burr and generalised gamma distributions. This paper extends the GB2 family to the contaminated GB2 family, which offers many flexible features, including bimodality and a wide range of skewness and kurtosis. Properties of the contaminated distribution are derived and evaluated in a simulation study and the suitability of the contaminated GB2 distribution for actuarial purposes is demonstrated through two real loss data sets. Analysis of tail quantiles for the data suggests large differences in extreme quantile estimates for different loss distribution assumptions, showing that the selection of appropriate distributions has a significant impact for insurance companies.