多元分布

NMath Stats contains a data table class with functions for computing descriptive statistics, such as mean, variance, standard deviation, percentile, median, quartiles, geometric mean, harmonic mean, RMS, kurtosis, skewness, and many more; PDF, CDF, inverse CDF, and random variable moments for a variety of probability distributions, including normal, Poisson, chi-square, gamma, beta, Student's t, F, binomial, and negative binomial; Combinatorial functions, such as factorial, log factorial, binomial coefficient, and log binomial; Multiple linear regression; Basic hypothesis tests, such as z-test, t-test, and F-test, with calculation of p-values, critical values, and confidence intervals; One-way and two-way analysis of variance and analysis of variance with repeated measures; Multivariate statistical analyses, including principal component analysis and hierarchical cluster analysis.

nmath统计包含一个数据表的阶层与职能计算描述性统计，如平均，方差，标准差，百分位，中位数， 25 ％，几何平均数，调和的意思是，有效值，峭度，偏度，还有更多的； PDF格式，民防部队，逆民防部队，并随机变量矩的各种概率分布，包括正常，泊松，卡方检定，伽玛，测试版，学生的吨，男，二项式，并负二项分布；组合的功能，例如阶乘，日志阶乘，二项式系数，并登入二项式；多元线性回归；基本假设测试，如的Z测试， t检验， F检验，计算p值，临界值，和置信区间；之一，双向和双方法方差分析和方差分析与反复的措施；多元统计分析，包括主成分分析和聚类分析。

If there exist a family of copulas, we could construct any bivariate or multivariate distribution functions of given margins by Sklars theorem and these distributions are always very useful for simulation.

如果我们有一族copula，那么根据Sklar定理，可以构造出任何指定边缘分布的二元或多元联合分布函数，而这些分布函数在建模与模拟方面是非常有用的。

The paper focuses on the multivariate Laplacian distribution. Based on MLD, we have obtained the variance of the quadric form, the covariance of two quadric forms and the covariance of the linear function and the quadric form.

对于多元拉普拉斯分布，我们推导出了多元拉普拉斯分布的二次型的方差，两个二次型的协方差，线性函数与二次型的协方差。

The next two chapters are the main content. From empirical distribution function, using theory of spline function , give new algorithms of monad distribution function and multivariate distribution function separately.

第三章和第四章由经验分布函数出发，利用B—样条函数理论，分别给出构造一元分布函数和多元分布函数的方法。

In order to reduce calculation error, the frequency distribution of average values is used to compute the mixed distribution's digital features of each component distribution, thereinto, the number of the component distribution is determined by AIC, choose the number that meets the minimum value of AIC as the component number of mixed distribution, and the other parameters are estimated by EM algorithm; Secondly, because each component distribution is corresponding to a kind of major gene genotype, according to the values of the average and variance of the each component distribution, we can use the limit error of the normal distribution to plot each individual into the correspondent component distribution, namely into correspondent major gene genotype. Then we regard each major gene genotype as a treatment level of one-way analysis of variances, and the one-way multivariate analysis of variance is carried out to calculate the covariance matrix of major gene effect, covariance matrix of polygene effect, covariance matrix of environment effect and so on; At last, combining the weights of the each component distribution of mixed distribution, we can calculate the variance of major gene effect, the variance of polygene effect, environmental variance and the genetic gain of the quantitative trait.

为减小计算误差，本研究采用均值的频数分布来计算各成分分布的数字特征，其中成分分布个数根据AIC准则，选择使AIC值达到最小的成分分布个数作为混合分布的成分分布数，分布中其它参数的确定利用EM算法来估计；其次，每个成分分布对应一种主基因基因型，根据各个成分分布的均值和方差，利用正态分布的极限误差将每个个体划分到相应的成分分布中，即相应的主基因基因型中，将每种主基因型作为单因素方差分析的一个处理水平，对其进行单因素的多元方差分析，分别计算主基因效应协方差阵、多基因效应协方差阵、环境协方差阵等参数；最后结合混合分布中各成分分布的权重即各主基因基因型的分离比例，计算主基因效应方差，多基因效应方差和环境方差，以及遗传力等参数，进而计算该数量性状的遗传进展。

Using the characteristic found,the maximum likelihood estimators and the moment estimator s of parameters of the multivariate exponential distribution of Freund are obtained.

利用分布密度分拆的思想，导出了二元及多元Freund型指数分布的一个特征，利用该特征，获得了二元及多元Freund型指数分布参数的最大似然估计及矩估计，还给出了强度服从二元Fre-und型指数分布时并联结构系统的可靠度估计及模拟。

The relations between multivariate Poisson distribution and multinomial distribution or multivariate normal distribution are given.

最后给出了多元Poisson分布与多项分布以及多元正态分布之间的关系。

Not only the non-linear dependence between financial markets is able to be caught, but also the more flexible multivariate distribution which can be use to analyze portfolio VaR is able to be obtained from this model.

该模型不仅能够得到金融市场间的非线性相关性，而且可以得到更灵活的多元分布，进而用于资产投资组合VaR分析。

The anti-sloughing mechanisms of modified polyalcohol were studied deeply through experiments including rolling and dispersing recovery,zeta potential and particle size distribution measuring,adsorption and .

通过降解和阳离子化反应，研制出了抑制性好而增粘负效应较低的改性多元醇防塌剂SD-306；通过红外光谱分析了改性多元醇防塌剂的分子结构，证明阳离子化反应引入了正氮基团；通过滚动分散、电动电位测量、粒度分布测量、吸附以及压力传递等实验手段，探讨了改性多元醇防塌剂的作用机理。

But when a rectangular continuous data set appears to have a longer tailed than normal distribution or it contains some values that are influential on statistical inference with normal distribution, the multivariate t distribution becomes useful for multiple imputations as an alternative to the multivariate normal distribution.

在多重插补法的基础上，当一个矩形连续数据集看起来有一个比正态分布还长的尾巴，或者是它包含了一些对正态分布的统计推断有影响的数据，多元t分布作为多元正态分布的替代分布，对于多重插补来说变的很有用了。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。