分布矩

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。

For verifying the proposed approach, the EEG potential simulated from current dipoles in an ideal homogeneous medium are generated. The localization discrepancy and the moment orientation discrepancy are used as index for measuring the estimation accuracy.

为了验证这里所提出方法的正确性，脑波模拟讯号是由电偶极在理想的均匀介质头颅模型下所得到；定位偏移量及偶极矩方向偏移量两参数被用来当做估计值准确度的指标，另外，初始值估计法的偏移量分布可用数学中的珈玛方程式描述出分布的特性。

Fri particular, the Wittmann-type strong law of larg numbers for independent random variables is generalized to the case of NA random variables. We also present the sufficient and necessary condition of the laws of logarithm, and we extend Teicher-type strong law of the large numbers for sequence of NA random variables. Some of the laws of iterated logarithm of Teicher-type, Egorov-type arid Wittmann-type for sequence of NA random variables are obtained. Then we investigate the rate3f ionvergcll( fbr series of NA randonl variables, we obtain soIne results fbr tl1e Iaws of theiterated logarithttl, the laws of logarithm and decreasing order fOr the tail sum.Risk itllttlysis tlleory is a sigIlifica11t part of insurance InatheInatics.

Wittmann（1985a）关于实独立随机变量列的结果，并给出了NA列强大数律成立的若干条件，特别建立了一般NA列对数律成立的充分必要条件，在二阶矩存在的条件下完整的解决了一般NA列对数律的问题，中文摘要2而已有的一些NA列对数律的结果可以由它推出，给出了NA列的Teiclier型强大数律，表明lbiChCI·（1979）给出的实独立随机变量列的强大数律可以减弱其条件等；建立厂不问分布NA列的Teicfl仪；Egorov，Petrov型有界重对数律，以及加权同分布NA列的有界重对数律，进一步推广了NA列的Kolmogory有界重对数律等，特别对NA列建立了Wittm洲型有界重对数律，而其证明方法与独立情形有很大不同，同时通过反例表明在与独立场合类似的条件下，独立列的Wittmann有界重对数律不能完美的推广到NA歹小惰形；最后研究了NA随机变量级数的收敛速度，给出了尾和下降的阶；尾和的有界重对数律，及尾和对数律成立的充要条件等，并通过反例说明 NA随机变量级数与独立随机变量级数在收敛速度方面存在的差异。

Since the concept of NA have a lot of applications in multivariate statistical analysis, reliability theory and percolation theory, various aspects of NA are significant and have been investigated by a host of scholars Fist, we give some Fuk-Nagaev type probability inequalities, moment inequalities of maximal partial sum for sequence of NA random variables, and some strong law of large numbers and complete convergence for sequence of NA random variables are obtained.

在本论文中我们对不要求强平稳或同分布的NA随机变量列进行了多方面的研究：首先对NA列建立了一组具有NA特点的关于最大部分和的Fuk-Nagaev型概率不等式及其关于某一类特定函数的矩不等式，它们在后续给出的极限定理的证明中发挥着重要作用；研究了具有不同分布的NA列的强收敛性，如对NA列建立了更一般条件下的Wittmann型强大数律及完全收敛性，同时也进一步改进了R。

Results Under the condition of the conjugate prior distribution, the prior parameters computed by three methods were similar.

结果在共轭先验分布的条件下，先验矩、分位数、众数与分位数三种方法确定的先验分布参数结果一致。

We mainly detected the TOF and angular distribution of photofragment, and get the anisotropy parameter β and the translational energy distribution. In addition, we calculated the geometries of the ground states, the excited states and the triplet excited states, and the transition electric dipole moments. According to these, the dissociation lifetimes of some molecules are calculated.

主要是探测了光解碎片的时间飞渡谱和角分布并通过前向卷积方法拟合得到了各向异性参数β和光解碎片的平动能分布；此外还用从头计算方法计算了反应物分子的基态、激发态、三重激发态的平衡几何构型和分子的跃迁偶极矩并据此计算了一部分分子的解离态寿命。

The Monte Carlo simulation shows that the present method is better than the Method of Moment in unbiasedness, and is generally comparable to MOM in efficiency.

对P-Ⅲ型总体分布，本文提出的权函数能使σ和Cs的估计由原方法的二阶加权中心矩降低为一阶加权中心矩估计。

Their adsorption rate on the molecular sieve catalysts surface and the stability of their carbonium ions were then obtained based on the molecular simulation on these molecules from their dipole moment, 2-dimensional electrostatic potential energy contours and 3-dimensional electrostatic potential energy isosurface.

采用半经验的AM1量子化学计算方法和静态理论，分别考察了噻吩、 3 甲基噻吩和 2 ，5 二甲基噻吩分子结构特性的不同，从偶极矩、各自垂直于芳香环平面的二维电势能分布曲线和整个分子周围三维电势能分布情况等方面分析了它们在分子筛催化剂表面吸附速度的快慢和生成正碳离子稳定性的高低，进一步比较了噻吩及其衍生物所生成的正碳离子进一步反应的能量变化，从而可判断噻吩及其衍生物裂化脱硫速度的快慢，噻吩及其衍生物裂化脱硫的速度由大到小分别为：2 ，5 二甲基噻吩、 3 甲基噻吩、噻吩。

The transition dipole moments of neutral and charged Green1 are compared using 3D transition density, which reveal the orientation and strength of transition dipole moments. The charge redistribution of neutral and charged Green1 upon excitation are shown and compared with 3D charge difference density. The electron-hole coherences of neutral and charged Green1 upon excitation are investigated with 2D site representation.

用3D跃迁密度方法对中性和带电的Green1的跃迁偶极矩进行比较，可显示出跃迁偶极矩的取向和强度；用3D电荷差异密度方法显示出激发后的中性和带电的Green1电荷重新分布，也进行了比较：用2D实空间分析方法来研究中性和带电的Green1处于激发态时的电子空穴相干性。

The results show that the number of the squeezed atomic dipoles is decided by the coherence of the atom, the direction of the quantum information entropy squeezing is decided by the phases of the field and the atom, and the quantum information entropy squeezing is a precision tool for the squeezing of the atom, especially when the atom is in the eigenstates of the dipole operators.

结果表明：原子偶极矩分量出现信息熵压缩的数目依赖于原子的分布角；信息熵压缩的方向由原子和场的位相决定；量子信息熵是原子压缩的精密量度工具，尤其适合于原子处在偶极矩算符的本征态时压缩情况的描述。

I use an example quoted by Hu Jiaqi:"It is reported that America separates the DNA of a kind of virus by making use of genetic technology and combines it with another kind of DNA. Finally, they get a kind of virulent biological agent called a "pyrotoxin". Someone discloses in private that 20 grams of such a kind of biological agent could result in the global death of 6 billion people due to infection."

我在这里例举胡家奇所引用过的例子："据报道，美国利用转基因技术，将一种病毒的DNA分离出来，与另外一种DNA进行结合，拼结成一种剧毒的"热毒素"生物战剂，且私下有人透露，这种生物战剂只需20克，就可以导致全球60亿人全部感染死亡。"

Waiting, for the queers and the coons and the Reds and the Jews.

等待着疯子和黑人还有红色共产主义者还有犹太人