计算二维正态分布的导函数拟合法

Derivative Fitting Procedure for Computing Bivariate Normal Distribution

根据二维正态分布的累积函数Ｂ对相关系数ｐ的导函数为已知这一重要性质，提出了用ｐ的多项式逼近Ｂ的号函数拟合法和改善计算精度的降ｐ措施．与数值积分法相比，计算效率显著提高，概念明确，方法简便，这对于使用高阶边界法门来提高可靠性分析的精度，很有实用意义．

The derivative of bivariate normal cumulative distribution function B with respect to its correlated coefficient p is a known function. According to this property, B can be quite accurately and even very accurately expressed as a polynomial of p. In order to improve the fitting accuracy, the p reduction technique is proposed. It reduces the polynomial expansion interval from [0,1] to [0,0.75]. Numerical calculations show that the procedure is of high accuracy and efficiency as compared with numerical integration method. So it will have practical applications in the reliability analysis when using high order boundslll.