非高斯型互相关随机数的发生技术

在用蒙特卡罗法进行仿真研究（例如进行测量不确定度评定）时,常常需要发生多个非高斯型互相关的随机数.就这一问题,给出完整的解决方案：用Hermite展开式生成近似的非高斯变量,借助Cholesky分解建立各变量之间的相关性.方法的关键在于对互相关系数矩阵进行“预变形”,使Cholesky分解也适用于非高斯变量.此外,还利用Cholesky分解式下三角矩阵的特点,对矩调整和建立相关性两个过程进行解耦.给出了详细的算法说明.

Generation Method of Correlated Non-Gaussian Random Variables

In Monte Carlo simulation such as the measurement uncertainty evaluation, it is often necessary to generate correlated multi-non-Gaussian random observations. This paper presents a complete solution to this problem; approximately generating the non-Gaussian variable by the Hermite development, and setting up the cross-correlations between each variable-pair with the help of Cholesky decomposition. The key idea is the pre-deformation of the correlation-coefficient-matrix, which lets the Cholesky decomposition also be suitable to non-Gaussian variables. Besides, according to the characteristics of the under-triangle matrix of the Cholesky decomposition, the process of moment adjusting and correlation establishment are uncoupled. The whole algorithm is explained in detail.