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两个n维随机变量函数的概率密度的求法 总被引:1,自引:0,他引:1
从二维随机变量函数的概率密度的求法出发,引入了n维随机变量函数的概率密度的求法,并介绍了两个常见的n维随机变量函数的概率密度的求法. 相似文献
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探讨了二维随机变量服从正态分布的一个充分条件.在两个不相关的随机变量的任意正整数线性组合都是正态随机变量的条件下,利用矩生成函数证明了它们分别服从正态分布,且联合分布也是二维正态分布. 相似文献
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二维离散随机变量相互独立的充要条件是其联合概率矩阵的秩为1;二维连续型随机变量相互独立的充要条件是其联合密度函数可分离变量. 相似文献
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本文讨论基于二维随机变量递增速度快慢的刻画及描述问题.引入和谐函数的概念,并利用和谐函数对二维随机变量和谐度量指标的定义进行改进,使得对二维随机变量之间和谐关系的研究更进一步.此外,借助于连接函数得到和谐函数的性质和计算公式,并将其应用到具体实例,借助和谐函数的图形进一步验证和谐函数的性质和主要结论. 相似文献
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给出二维随机变量独立性的一个简易判别法,证明其存在的合理性,并将其推广至n维随机变量及其函数独立性的判别. 相似文献
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将文献[1]给出的由一维连续型随机变量的概率密度函数构造二维连续型随机变量的概率密度函数的方法,推广为由一维连续型随机变量的概率密度函数构造三维连续型随机变量的概率密度函数的情况,并作出了证明和举例说明.说明利用本文的方法构造多维概率密度函数,其方法简单易行. 相似文献
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Gregory J. Morrow 《Probability Theory and Related Fields》1987,75(1):87-95
Summary The central limit theorem for stationary linearly dependent sequences is extended for elements in the space of continuous functions on a compact metric space. The proof is based on a new estimate for exponential-type moments of sums of independent random variables. 相似文献
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M. V. Myronyuk 《Ukrainian Mathematical Journal》2008,60(9):1437-1447
According to the well-known Skitovich-Darmois theorem, the independence of two linear forms of independent random variables
with nonzero coefficients implies that the random variables are Gaussian variables. This result was generalized by Krakowiak
for random variables with values in a Banach space in the case where the coefficients of forms are continuous invertible operators.
In the first part of the paper, we give a new proof of the Skitovich-Darmois theorem in a Banach space. Heyde proved another
characterization theorem similar to the Skitovich-Darmois theorem, in which, instead of the independence of linear forms,
it is supposed that the conditional distribution of one linear form is symmetric if the other form is fixed. In the second
part of the paper, we prove an analog of the Heyde theorem in a Banach space.
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 9, pp. 1234–1242, September, 2008. 相似文献
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E. I. Ostrovskii 《Journal of Mathematical Sciences》1992,61(1):1901-1905
This note is devoted to the generalization of a limit theorem on sums of strongly dependent random variables (non-central limit theorem) to the case when the initial Gaussian sequence, functions of which are considered, assumes values in the Banach space of continuous functions on a compactum; special attention is given to the transition case, when the limit distribution changes by a jump.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 177, pp. 114–119, 1989. 相似文献
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Stochastic versions of the extension theorems of Tietze and Dugundji are obtained, as well as an existence theorem for partitions of unity by random continuous functions. A form of the classical approximation theorem of Mergelyan valid for random holomorphic functions on random compact sets is presented. A similar approach yields versions of the approximation theorems of Runge, Arakelyan, and Vitushkin.Research of both authors was partially supported by the NSF under Grant No. DMS 85-02308 相似文献
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E. A. Baklanov 《Siberian Mathematical Journal》2006,47(6):975-979
We prove the strong law of large numbers for the linear combinations of functions of order statistics (L-statistics) based on weakly dependent random variables. We also establish the Glivenko-Cantelli theorem for ?-mixing sequences of identically distributed random variables. 相似文献
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Eugenio P. Balanzario Jorge Sánchez-Ortiz 《Statistics & probability letters》2010,80(23-24):1713-1719
We present two sufficient conditions for an absolutely continuous random variable to obey Benford’s law for the distribution of the first significant digit. These two sufficient conditions suggest that Benford’s law will not often be observed in everyday sets of numerical data. On the other hand, we recall that there are two processes by way of which a random variable can come close to following Benford’s law. The first of these is the multiplication of independent random variables and the second is the exponentiation of a random variable to a large power. Our working tool is the Poisson sum formula of Fourier analysis. Like the central limit theorem, Benford’s law has an asymptotic nature. 相似文献
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Filipe J. Marques M. Theodor Loots Andriëtte Bekker 《Mathematical Methods in the Applied Sciences》2019,42(17):5718-5735
Series representations for several density functions are obtained as mixtures of generalized gamma distributions with discrete mass probability weights, by using the exponential expansion and the binomial theorem. Based on these results, approximations based on mixtures of generalized gamma distributions are proposed to approximate the distribution of the sum of independent random variables, which may not be identically distributed. The applicability of the proposed approximations are illustrated for the sum of independent Rayleigh random variables, the sum of independent gamma random variables, and the sum of independent Weibull random variables. Numerical studies are presented to assess the precision of these approximations. 相似文献
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本文引进对数似然比作为任意离散随机变量序列相依性的一种度量,并通过限制似然比给出样本空间的某种子集,在这种子集上得到了离散随机变量序列的一类强极限定理,它包含若干经典强大数定律为其特例.在证明中本文提出了证明强极限定理的一种分析方法,其要点是将关于单调函数可微性的定理应用于几乎处处收敛的研究. 相似文献