共查询到20条相似文献,搜索用时 78 毫秒
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基于多元正态分布和一元正态分布之间的一个重要性质,将其应用于问题求解,实例说明,巧妙借助该性质可使相关问题的求解过程大为简化. 相似文献
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通过对正、余弦函数无穷乘积展开式先取对数,再求导或再积分的方法,可获得两类无穷级数的和以及两类积分的无穷级数表示. 相似文献
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本文应用正态分布的线性不变性来研究二维正态分布的性质,包括可加性、边际分布、特征函数、条件分布、条件数学期望. 相似文献
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讨论了用泊松分布和正态分布近似表示二项分布的精确程度问题,对于泊松分布,指出了它对二项分布B(n,p)的概率值的近似精确与否基本上只依赖于参数p而不依赖于n,并说明了经验条件“np≤5”的不确切. 相似文献
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M.R. Leadbetter G. Lindgren H. Rootzén 《Stochastic Processes and their Applications》1978,8(2):131-139
The asymptotic distribution of the maximum Mn=max1?t?nξt in a stationary normal sequence ξ1,ξ,… depends on the correlation rt between ξ0 and ξt. It is well known that if rt log t → 0 as t → ∞ or if Σr2t<∞, then the limiting distribution is the same as for a sequence of independent normal variables. Here it is shown that this also follows from a weaker condition, which only puts a restriction on the number of t-values for which rt log t islarge. The condition gives some insight into what is essential for this asymptotic behaviour of maxima. Similar results are obtained for a stationary normal process in continuous time. 相似文献
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Serge B. Provost Edmund M. Rudiuk 《Annals of the Institute of Statistical Mathematics》1996,48(2):381-394
The exact density of the difference of two linear combinations of independent noncentral chi-square variables is obtained in terms of Whittaker's function and expressed in closed forms. Two distinct representations are required in order to cover all the possible cases. The corresponding expressions for the exact distribution function are also given. 相似文献
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The tetrachoric series is a technique for evaluating multivariate normal probabilities frequently cited in the statistical literature. In this paper we have examined the convergence properties of the tetrachoric series and have established the following. For orthant probabilities, the tetrachoric series converges if , 1 ≤ i < j ≤ k, where ?ij are the correlation coefficients of a k-variate normal distribution. The tetrachoric series for orthant probabilities diverges whenever k is even and or k is odd and , 1 ≤ i < j ≤ k. Other specific results concerning the convergence or divergence of this series are also given. The principal point is that the assertion that the tetrachoric series converges for all k ≥ 2 and all ?ij such that the correlation matrix is positive definite is false. 相似文献
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Let X1, X2, …, Xn be i.i.d. d-dimensional random vectors with a continuous density. Let
and
. In this paper we find that the distribution of Zk (or Yk) can be used for characterizing multivariate normal distribution. This characterization can be employed for testing multivariate normality in terms of the so-called transformation method. 相似文献
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Hung C. Li 《Journal of multivariate analysis》1978,8(2):255-261
Let Xj (j = 1,…,n) be i.i.d. random variables, and let Y′ = (Y1,…,Ym) and X′ = (X1,…,Xn) be independently distributed, and A = (ajk) be an n × n random coefficient matrix with ajk = ajk(Y) for j, k = 1,…,n. Consider the equation U = AX, Kingman and Graybill [Ann. Math. Statist.41 (1970)] have shown U ~ N(O,I) if and only if X ~ N(O,I). provided that certain conditions defined in terms of the ajk are satisfied. The task of this paper is to delete the identical assumption on X1,…,Xn and then generalize the results to the vector case. Furthermore, the condition of independence on the random components within each vector is relaxed, and also the question raised by the above authors is answered. 相似文献
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Rasul A. Khan 《Journal of multivariate analysis》1978,8(4):550-558
Let X1, X2,… be idd random vectors with a multivariate normal distribution N(μ, Σ). A sequence of subsets {Rn(a1, a2,…, an), n ≥ m} of the space of μ is said to be a (1 − α)-level sequence of confidence sets for μ if P(μ Rn(X1, X2,…, Xn) for every n ≥ m) ≥ 1 − α. In this note we use the ideas of Robbins Ann. Math. Statist. 41 (1970) to construct confidence sequences for the mean vector μ when Σ is either known or unknown. The constructed sequence Rn(X1, X2, …, Xn) depends on Mahalanobis'
or Hotelling's
according as Σ is known or unknown. Confidence sequences for the vector-valued parameter in the general linear model are also given. 相似文献
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In [1] K. A. S. Abdel-Ghaffar derives a lower bound on the probability of undetected error for unrestricted codes. The proof relies implicitly on the binomial moments of the distance distribution of the code. We use the fact that these moments count the size of subcodes of the code to give a very simple proof of the bound in Abdel by showing that it is essentially equivalent to the Singleton bound. This proof reveals connections of the probability of undetected error to the rank generating function of the code and to related polynomials (Whitney function, Tutte polynomial, and higher weight enumerators). We also discuss some improvements of this bound.Finally, we analyze asymptotics. We show that an upper bound on the undetected error exponent that corresponds to the bound of Abdel improves known bounds on this function. 相似文献
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Sigeo Aki 《Annals of the Institute of Statistical Mathematics》1985,37(1):205-224
Summary This paper considers discrete distributions of orderk based on a binary sequence which is defined as an extension of independent trials with a constant success probability and
is more practical than the independent trials. Some results on calculation of probabilities and characteristics of the distributions
are obtained as well as their formal expressions. Examples and an application are also given.
The Institute of Statistical Mathematics 相似文献