二元正态分布函数(Coons曲面法)插值研究

根据Coons曲面生成原理，给出了二元正态(Gauss)分布的插值方法。对于二元正态分布密度函数，仅需给定插值区域边界上的值，即可插值出该区域上任意一点密度函数值；对于二元正态分布函数，仅需给定插值区域两边的双边界值，即可得到该区域上任意一点分布函数值。该方法无需知道也无需计算出Gauss分布函数的各项参数，便于应用，插值结果精确，绝对误差为O(10＾－9)，相对误差为O（10＾－11）。

Study on Interpolation of Bivariate Normal Distribution with Coons Surface Method

The interpolation method of bivariate normal (Gauss) distribution with the principles of creating a Coons surface is presented. Based on the given values of bivariate normal distribution density function on the boundary of a rectangular region, the values of the density function on the rectangular region can be obtained. With the given values of bivariate normal distribution function on the two biboundaries of a rectangular region, the values of distribution function on the rectangular region can be found. This method features that the values of a normal distribution (or density) function on a field only dependent on its values on the boundary of the field, not on any parameters of the distribution function. In practice, it has higher precision: the absolute error is O (10-9) and the relative error is O (10-11).