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<p>Effective 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 find 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 fields 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 five actuarial indicators have been applied under the new family. We made a comprehensive application on reinsurance revenue data. The new family showed great flexibility in dealing with actuarial risks and its statistical analysis.</p>

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A novel weighted family for the reinsurance actuarial risk analysis with applications

  • 期刊论文

  • 发表日期：

    2025年7月14日

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  • Fazlollah Lak,
  • Morad Alizadeh,
  • Danial Mazarei,
  • Reza Sharafdini,
  • Ali Dindarlou,
  • Haitham M. Yousof

摘要

Effective 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 find 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 fields 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 five actuarial indicators have been applied under the new family. We made a comprehensive application on reinsurance revenue data. The new family showed great flexibility in dealing with actuarial risks and its statistical analysis.