Actuarial Measures, Regression, and Applications of Exponentiated Fréchet Loss Distribution

Abstract

In this study, a new loss distribution, called the exponentiated Fréchet loss distribution is developed and studied. The plots of the density function of the distribution show that the distribution can exhibit different shapes including right skewed and decreasing shapes, and various degrees of kurtosis. Several properties of the distribution are obtained including moments, mean excess function, limited expected value function, value at risk, tail value at risk, and tail variance. The estimators of the parameters of the distribution are obtained via maximum likelihood, maximum product spacing, ordinary least squares, and weighted least squares methods. The performances of the various estimators are investigated using simulation studies. The results show that the estimators are consistent. The new distribution is extended into a regression model. The usefulness and applicability of the new distribution and its regression model are demonstrated using actuarial data sets. The results show that the new loss distribution can be used as an alternative to modelling actuarial data.