New Weibull-Pareto Poisson distribution: properties, actuarial measures and applications

A new power series distribution called the new Weibull-Pareto Poisson distribution is developed. The proposed model is very flexible in modelling heavy-tailed data. Some of the statistical properties are also derived and these include moments, moment generating function, and Rényi entropy. We derive the maximum likelihood estimates of the model parameters. We also derive risk measures, conduct and present their numerical simulations. Numerical simulations results for actuarial risk measures show that the new developed model is heavy-tailed compared to its nested models and some competing models. A Monte Carlo simulation study was also conducted to evaluate the consistency of the model parameter estimates. The results from this study confirm that the developed model produce consistent and reliable parameter estimates. Two heavy-tailed real data examples are used to demonstrate the usefulness of the new proposed model.