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<p>The Arctan Marshall-Olkin family is introduced as an innovative and adaptable class of heavy-tailed distributions for modeling extreme events in financial and economic sciences. This family emerges from the combination of the Marshall-Olkin framework with the Arctan-X approach, which leverages the arctangent inverse trigonometric function. A particular case, the Arctan-Marshall-Olkin-Weibull (ATMOW) distribution, is explored in detail. Unlike the conventional two-parameter Weibull distribution, ATMOW incorporates an additional parameter, enhancing its adaptability to heavy-tailed data. Monte Carlo simulations confirm the efficiency of the maximum likelihood estimation for parameter inference. Furthermore, closed-form expressions for key actuarial risk measures, including value at risk and tail value at risk, are derived to assess extreme financial risks. Empirical applications to real financial and economic datasets demonstrate better performance of ATMOW compared to several competing multiparameter distributions.</p>

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Modeling Economics and Finance Data with the Arctan Marshall-Olkin Weibull Distribution

  • 期刊论文

  • 发表日期：

    2025年6月12日

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  • Mintodê Nicodème Atchadé,
  • Espoir Zyad Kossou,
  • Théophile Otodji,
  • Mahoulé Jude Bogninou,
  • Aliou Moussa Djibril

摘要

The Arctan Marshall-Olkin family is introduced as an innovative and adaptable class of heavy-tailed distributions for modeling extreme events in financial and economic sciences. This family emerges from the combination of the Marshall-Olkin framework with the Arctan-X approach, which leverages the arctangent inverse trigonometric function. A particular case, the Arctan-Marshall-Olkin-Weibull (ATMOW) distribution, is explored in detail. Unlike the conventional two-parameter Weibull distribution, ATMOW incorporates an additional parameter, enhancing its adaptability to heavy-tailed data. Monte Carlo simulations confirm the efficiency of the maximum likelihood estimation for parameter inference. Furthermore, closed-form expressions for key actuarial risk measures, including value at risk and tail value at risk, are derived to assess extreme financial risks. Empirical applications to real financial and economic datasets demonstrate better performance of ATMOW compared to several competing multiparameter distributions.