A class of claim distributions: Properties, characterizations and applications to insurance claim data

Actuaries are often in search of finding an adequate model for actuarial and financial risk management problems. In the present work, we introduce a class of claim distributions useful in a number of lifetime analyses. A special sub-model of the proposed family, called the Weibull claim model, is considered in detail. Some mathematical properties along with certain characterizations are derived and maximum likelihood estimates of the model parameters are obtained. A simulation study has been carried out to evaluate the performance of the maximum likelihood estimators. Furthermore, some actuarial measures such as value at risk, tail value at risk, tail variance and tail premium variance are calculated. A simulation study based on these actuarial measures is done. Finally, two applications of the proposed model to the insurance claim data set are presented.