基于样本协方差矩阵的多维随机数生成方法

Multidimensional random number generating method based on the sample covariance matrix

对于概率模型未知的多维数据样本容量扩充问题,根据主成分分析原理以及多维正态分布的性质,讨论并给出了与已知多维样本数据有相同协方差结构的模拟数据生成算法,并在此基础上给出了变量的离散化处理方法.实现了在小样本数据基础上不改变变量间协方差结构的样本容量扩充,为小样本条件下的数学建模、检验和分析提供样本数据支撑.

For multidimensional data probability model of the unknown sample capacity expansion problem, according to the principle of principal component analysis and the properties of multidimensional Gaussian distribution, we discuss and give the multidimensional samples with known data simulation data with the same covariance structure generation algorithm, and we give the discretization processing method on the basis of the variables . We realize the expansion of sample capacity without changing the covariance structure between variables basing on small sample data. Furthermore, the algorithm supports the mathematical modeling, testing and analysis under the condition of small samples.