问题描述
我遇到了一个问题，我必须能够生成一组随机选择的一组多元正态分布，在Java中均值为0，并具有给定的3 * 3方差-协方差矩阵。
I've run into a problem where I have to be able to generate a set of randomly chosen numbers of a multivariate normal distribution with mean 0 and a given 3*3 variance-covariance matrix in Java.
是否有一种简便的方法？
Is there an easy way as to do this?
推荐答案
1）使用库
或者，如果您确实感到迫切需要自己做：
Or, if you really feel a burning need to do this yourself:
2）假设您要生成具有均值向量M和方差/协方差矩阵V的法线，请执行在V上得出下三角矩阵L，使得V = LL （上标t表示转置）。生成三个独立标准法线的向量Z（使用 Random.nextGaussian（）来获取单个元素）。然后 LZ + M 将具有所需的多元正态分布。
2) Assuming you want to generate normals with a mean vector M and variance/covariance matrix V, perform Cholesky Decomposition on V to come up with lower triangular matrix L such that V=LL (where the superscript t indicates transpose). Generate a vector Z of three independent standard normals (using Random.nextGaussian() to get the individual elements). Then LZ + M will have the desired multivariate normal distribution.
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