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<p>This study introduces a novel statistical family known as the Ristić-Balakrishnan-Heavy-Tailed-Type II Topp-Leone-G (RB-HT-TIITL-G). The research explores key statistical properties, including hazard rate function, quantile function, moments, stochastic ordering, and order statistics. Furthermore, essential risk measures such as value at risk, tail variance, and tail variance premium are derived. Several parameter estimation methods, including maximum likelihood, least squares, weighted least squares, maximum product spacing, Cramér-von Mises, and Anderson-Darling estimators, are applied. Monte Carlo simulations evaluate the consistency of these estimation techniques. Lastly, the model’s effectiveness is validated using real-world data, demonstrating its suitability for modeling diverse data sets.</p>

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The New Ristić-Balakrishnan-Heavy-Tailed-Type II Topp-Leone-G Family of Distributions with Applications

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月27日

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  • Gayan Warahena-Liyanage,
  • Broderick Oluyede,
  • Thatayaone Moakofi

摘要

This study introduces a novel statistical family known as the Ristić-Balakrishnan-Heavy-Tailed-Type II Topp-Leone-G (RB-HT-TIITL-G). The research explores key statistical properties, including hazard rate function, quantile function, moments, stochastic ordering, and order statistics. Furthermore, essential risk measures such as value at risk, tail variance, and tail variance premium are derived. Several parameter estimation methods, including maximum likelihood, least squares, weighted least squares, maximum product spacing, Cramér-von Mises, and Anderson-Darling estimators, are applied. Monte Carlo simulations evaluate the consistency of these estimation techniques. Lastly, the model’s effectiveness is validated using real-world data, demonstrating its suitability for modeling diverse data sets.