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Normal transformation for correlated random variables based on L-moments and its application in reliability engineering

机译：基于L-MOCENTS的相关随机变量的正常变换及其在可靠性工程中的应用

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摘要

In this paper, a new method for normal transformation is proposed to transform correlated non-normal random variables into independent standard normal ones based on their first four linear moments (L-moments), standard deviations and correlation matrix. The complete monotonic expressions of the equivalent correlation coefficient are proposed and the applicable range of the original correlation coefficient to ensure the transformation's executability is identified. Numerical studies demonstrate that the admissible range of the normal transformation for correlated random variables based on L-moments is larger in scope than that based on ordinary central moments (C-moments), and the proposed method is effective for normal transformations and sufficiently accurate for reliability engineering practices.
机译：在本文中，提出了一种新的正常变换方法，以基于其前四个线性时刻（L-MOCENTS），标准偏差和相关矩阵将相关的非正常随机变量转换为独立标准正常变量。提出了等效相关系数的完整单调表达式，并确定了原始相关系数的适用范围，以确保转换的可执行性。数值研究表明，基于L-MOCENTS的相关随机变量的允许范围比基于普通中央矩（C矩）更大，并且所提出的方法对于正常变换是有效的，并且足够准确可靠性工程实践。

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