Analyzing Insurance Data with an Alpha Power Transformed Exponential Poisson Model

In this paper, we propose a new model by adding an additional parameter to the baseline distributions for modeling claim and risk data used in actuarial and financial studies. The new model is called alpha power transformed exponential Poisson model. It has three parameters and its probability density function can be skewed and unimodal. Several distributional properties of the proposed model such as reliability, hazard rate, quantile and moments are established. Estimation of the unknown parameters based on maximum likelihood estimation are derived and risk measures such as value at risk and tail value at risk are computed. Moreover, the performance of these measures is illustrated via numerical simulation experiments. Finally, two real data sets of insurance losses are analyzed to check the potential of the proposed model among some of the existing models.