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首先基于等效相关系数的传统二维积分方程,引入二维相关标准正态密度函数的Mehler级数展开公式,然后导出了等效相关系数的无穷次代数方程及其收敛特性,实现了积分方程向代数方程的转变,进一步完善了Nataf变换理论.同时,通过方程截断近似的方式给出了求解等效相关系数的迭代方法.由于避免了二维相关标准正态密度函数的积分和利用了代数方程系数的可重复性及一维积分特性,本文方法具有广泛的适用范围,且兼顾了计算的精度和效率.最后,通过算例验证了方法的有效性和精确性.
Firstly, based on the traditional two-dimensional integral equation with equivalent correlation coefficient, the Mehler series expansion formula of normalized density function of two-dimensional correlation standard is introduced. Then the infinite number of algebraic equations of equivalent correlation coefficient and its convergence property are derived, and the integral equation The transformation to algebraic equation further improves the Nataf transformation theory. At the same time, an iterative method for solving the equivalent correlation coefficient is given by means of the truncation approximation of the equation. Since the integral of the two-dimensional correlation standard normal density function is avoided and the algebra The reproducibility of the coefficient of the equation and the one-dimensional integral characteristic, the method has a wide range of applicability and takes into account the accuracy and efficiency of the calculation.Finally, the validity and accuracy of the method are verified by an example.