论文标题
线性时间和恒定空间，算法以计算多元正常分布的混合力矩
A Linear Time, and Constant Space, Algorithm to Compute the Mixed Moments of the Multivariate Normal Distributions
论文作者
论文摘要
使用从Apagodu-Zeilberger多元Almkvist-Zeilberger算法中获得的复发，我们提出了一个线性时间和恒定空间，算法，以使用任何特定的k来计算K-变量一般正态分布的一般混合矩，用于任何协方差矩阵。除了在统计数据中显而易见的重要性外，这些数字在枚举组合学方面也非常重要，因为它们以多种方式计算出具有不同性别的物种，一群人都可以结婚，并跟踪不同种类的异性恋婚姻。我们将算法（随附的枫木包装，mvnm.txt）实施了双变量和三分化案例（从而照顾我们自己的2个性别社会和一个假定的3个性别社会），但是，las，较大的k的实际复发时间太长了，我们对我们进行了太长时间的计算。我们将它们作为计算挑战。
Using recurrences gotten from the Apagodu-Zeilberger Multivariate Almkvist-Zeilberger algorithm we present a linear-time, and constant-space, algorithm to compute the general mixed moments of the k-variate general normal distribution, with any covariance matrix, for any specific k. Besides their obvious importance in statistics, these numbers are also very significant in enumerative combinatorics, since they count in how many ways, in a species with k different genders, a bunch of individuals can all get married, keeping track of the different kinds of heterosexual marriages. We completely implement our algorithm (with an accompanying Maple package, MVNM.txt) for the bivariate and trivariate cases (and hence taking care of our own 2-sex society and a putative 3-sex society), but alas, the actual recurrences for larger k took too long for us to compute. We leave them as computational challenges.
