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<p>Since its inception, the epsilon distribution has piqued the interest of statisticians. It has been successfully used to solve a variety of statistical problems. In this article, we propose to use the quadratic rank transmutation map mechanism to extend this distribution. This mechanism is not new; it was already used to improve the modeling capabilities of a number of existing distributions. For the original epsilon distribution, we expect the same benefits. As a result, we implement the transmuted epsilon distribution as a flexible three-parameter distribution with a bounded domain. We demonstrate its key features, focusing on the properties of its distributional mechanism and conducting quantile and moment analyses. Applications of the model are presented using two data sets. We also perform a regression analysis based on this distribution.</p>

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The transmuted epsilon distribution with applications in reliability engineering

  • 期刊论文

  • 发表日期：

    2025年6月26日

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  • Christophe Chesneau,
  • Hassan S. Bakouch,
  • Idika E. Okorie,
  • Bader Almohaimeed

摘要

Since its inception, the epsilon distribution has piqued the interest of statisticians. It has been successfully used to solve a variety of statistical problems. In this article, we propose to use the quadratic rank transmutation map mechanism to extend this distribution. This mechanism is not new; it was already used to improve the modeling capabilities of a number of existing distributions. For the original epsilon distribution, we expect the same benefits. As a result, we implement the transmuted epsilon distribution as a flexible three-parameter distribution with a bounded domain. We demonstrate its key features, focusing on the properties of its distributional mechanism and conducting quantile and moment analyses. Applications of the model are presented using two data sets. We also perform a regression analysis based on this distribution.