The Fleishman third‐order polynomial algorithm is one of the most‐often used non‐normal data‐generating methods in Monte Carlo simulations. At the crux of the Fleishman method is the solution of a non‐linear system of equations needed to obtain the constants to transform data from normality to non‐normality. A rarely acknowledged fact in the literature is that the solution to this system is not unique, and it is currently unknown what influence the different types of solutions have on the computer‐generated data. To address this issue, analytical and empirical investigations were conducted, aimed at documenting the impact that each solution type has on the design of computer simulations. In the first study, it was found that certain types of solutions generate data with different multivariate properties and wider coverage of the theoretical range spanned by population correlations. In the second study, it was found that previously published recommendations from Monte Carlo simulations could change if different types of solutions were used to generate the data. A mathematical description of the multiple solutions to the Fleishman polynomials is provided, as well as recommendations for users of this method.

中文翻译：

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关于Fleishman方法的解的多重性及其在仿真研究中的影响。

Fleishman三阶多项式算法是蒙特卡洛模拟中最常用的非正规数据生成方法之一。弗莱什曼方法的关键是求解方程组的非线性系统，该系统需要获取常数以将数据从正态转换为非正态。文献中很少有人承认的事实是，该系统的解决方案不是唯一的，并且目前尚不清楚不同类型的解决方案会对计算机生成的数据产生什么影响。为了解决这个问题，进行了分析和实证研究，目的是记录每种解决方案类型对计算机仿真设计的影响。在第一项研究中 结果发现，某些类型的解决方案会生成具有不同多元属性的数据，并且会覆盖总体相关性所涵盖的理论范围。在第二项研究中，发现如果使用不同类型的解决方案来生成数据，则先前发布的蒙特卡洛模拟建议可能会发生变化。提供了对Fleishman多项式的多个解决方案的数学描述，并为该方法的用户提供了建议。