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1.
Γ分布数字特征的应用王汉荣(沙洲职业工学院)众所周知,x2分布、F分布、t分布等在数理统计学中起着十分重要的作用,但由于它们的分布密度形式上比较复杂,因此,如果直接由分布密度出发去计算它们的数学特征,那么计算量很大。本文通过分布间的关系,利用。分布的...  相似文献   

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王炳章  方小娟 《数学进展》2002,31(5):467-475
本文研究了未知分布的逼近问题,利用随机加权法,给出了有Edgeworth展式的一类(未知)分布的模拟分布,证明了在一定条件下,模拟分布与未知分布的逼近精度达到O(n^-1√lnlnn),称之为随机加权逼近的重对数律。  相似文献   

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多重线性回归模型的贝叶斯预报分析是贝叶斯线性模型理论的重要组成部分。通过模型系统的统计结构,证明了矩阵正态-Wishart分布为模型参数的共轭先验分布;利用贝叶斯定理,根据模型的样本似然函数和参数的先验分布推导了参数的后验分布;然后,从数学上严格推断了模型的预报分布密度函数,证明了模型预报分布为矩阵t分布。研究结果表明:由于参数先验分布的作用,样本的预报分布与其原统计分布有着本质性的差异,前服从矩阵正态分布,而后为矩阵t分布。  相似文献   

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本文研究了与矩阵Г分布相关的若干分布的密度函数,利用矩阵Г分布的特征函数和它的Bartlett分解等方法,获得了与矩阵Г分布相关的几个分布的密度函数解析表达式,它们包括Г分布随机矩阵的子矩阵、行列式、迹和特征根的分布密度,进一步还得到了相关系数矩阵的分布密度函数形式.  相似文献   

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本文利用[3]中所给出的投影追踪经验分布的极限分布类的表示,通过几个例子说明了该分布类与对称的无穷可分分布类,Levy分布类与稳定分布类之间的关系  相似文献   

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本文利用(3)中所给出的投影追踪经验分布的极限分布数的表示,通过几个例子说明了该分布类与对称的无究可分分布类,Levy分布类与稳定分布类之间的关系。  相似文献   

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熵是一个分布的重要信息特征,通过对矩阵变量积分的一些技巧,利用矩阵r分布的特征,本文获得了矩阵F分布和矩阵Beta分布的熵.  相似文献   

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关于汽车赔付次数的一类新分布   总被引:4,自引:0,他引:4  
为了拟合汽车的赔付次数,本文给出了一类新的分布,即GPSJ1分布类.这个三参数的分布类包括的经典赔付次数分布比较多,特别是许多已知的无穷可分分布都属于这一类,在求参数的最大似然估计时此分布也具有很大的优越性,文中对此进行了讨论.本文最后我们以中国一家保险公司的实际赔付数据为例用此分布类对其进行了拟合,拟合效果令人满意。  相似文献   

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依分布律收敛与分布函数a·e收敛的关系方敏(北方交通大学)教材对于依分布律收敛的定义一般为:设随机变量ξn的分布函数是Fn,n=,2,…随机变量ξ的分布函数是F,若对F的每一连续点兄来说,Fn(x0)→F(x0),则称ξn的分布律收敛于ξ的分布律,记...  相似文献   

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复合Poisson过程参数的检验   总被引:6,自引:0,他引:6  
当风险为非同质时,索赔次数的分布可用复合Poisson过程来描述,Hofmann分布族可用于复合Poisson过程中索赔次数的研究,本文讨论了Hofmann分布的相参数的检验问题,得到了它的检验统计量及其渐近分布。  相似文献   

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We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.  相似文献   

13.
It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.  相似文献   

14.
As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years (2001-2005). The main topics are: convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.  相似文献   

15.
Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.  相似文献   

16.
张丽娜  吴建华 《数学进展》2008,37(1):115-117
One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the'living world. In his seminal paper "The Chemical Basis of Morphogenesis", Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates(1990) on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing's prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows  相似文献   

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<正>Submission Authors must use LaTeX for typewriting,and visit our website www.actamath.com to submit your paper.Our address is Editorial Office of Acta Mathematica Sinica,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China.  相似文献   

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