Ali Dindarloo

Efective descriptions and analyses of risk exposure can be performed using continuous G families of distributions. To illustrate the level of exposure to a certain actuarial danger, it is better to fnd a single value, or at least, a small set of values. In this paper, we present a new weighted family for applied purposes in the felds of statistical and actuarial modeling. We are motivated to present simulations in order to evaluate the behavior of the estimations of the maximum likelihood, weighted least squares, ordinary least squares, Cramer-von Mises, moments and Anderson-Darling right tail Anderson-Darling and methods. We will ignore the algebraic derivations and theoretical results of these methods since it is already present in a lot of statistical literature. Three applications were presented to verify the relevance and resilience of the new family. Five actuarial indicators were studied for risk assessment and analysis. The fve actuarial indicators have been applied under the new family. We made a comprehensive application on reinsurance revenue data. The new family showed great fexibility in dealing with actuarial risks and its statistical analysis.