广义正态分布及其二次函数的性质

Generalized Normal Distribution and Property of Its quadratic Function

利用随机向量的母函数定义广义正态分布，将正态随机向量的方差阵由满秩矩阵推广到降秩矩阵。根据母函数的性质，推导出正态分布向量的二次函数的数字特征，并将结果应用于误差传播，得到了非线性函数顾及二次项的误差传播公式的显式表达式。

The generalized normal distribution is defined by the generating function of stochastic vectors. and the variance matrix of normal stochastic vectors is spread from the full rank matrix to the singular matrix. According to the property of generating function, the digital feature of the quadratic function of normal stochastic vectors is inferred, and the result is applied to error propagation, the explicit expression of the error propagation formula with regard to the quadratic for non-linear function is obtained.