共查询到20条相似文献,搜索用时 10 毫秒
1.
A subset of Bernard's RD-model (replenishment-depletion) is considered from the viewpoint of the calculus of finite differences. The most general case is considered and includes an urn with balls of many colors, each color being replenished either deterministically or stochastically. Factorial moment generating functions (fmgfs) are employed to define probability generating functions. A new result is given for the two color case defining the fmgf and probability generating function (with probabilities) when the replenishments are positive valued random variables with given factorial moments. This result involves beta integral transforms defining a manifold of discrete distributions. Particular cases relate to hypergeometric discrete distributions.This research was partly supported by Martin Marietta Energy Systems, Inc., under contract DE-AC05-84OR21400 with the U.S. Department of Energy. 相似文献
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J. Šiaulys 《Acta Appl Math》2003,79(1-2):129-135
A characterization of a set of strongly additive functions f
x
with asymptotically finite support is obtained. Strongly additive functions which take the unit or zero values for each prime number p are considered. 相似文献
4.
This paper provides an organized history of well-poised hypergeometric series. The object is to reveal the process by which a rather narrow mathematical study blossomed into a topic of widespread importance. In addition, short biographies of the early contributors are included. 相似文献
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L. Loura 《Czechoslovak Mathematical Journal》2006,56(2):543-558
In this paper we use a duality method to introduce a new space of generalized distributions. This method is exactly the same
introduced by Schwartz for the distribution theory. Our space of generalized distributions contains all the Schwartz distributions
and all the multipole series of physicists and is, in a certain sense, the smallest space containing all these series.
To The Memory of Laurent Schwartz 相似文献
7.
An urn has balls of colors C1 and C2. It is replenished (R) by balls of both colors and then depleted by (D) the same number; this constitutes a cycle. When R = D, the system is closed and equilibrium will be reached after many cycles. The ultimate distribution is found only when the replenishment is the same for each color. Asymptotic normal and asymptotic binomial distributions arise when the parameters reach extreme values. For the multicolor urn an expression is given for the correlation between the number of balls of any two colors. 相似文献
8.
We study a generalized Friedman’s urn model with multiple drawings of white and blue balls. After a drawing, the replacement follows a policy of opposite reinforcement. We give the exact expected value and variance of the number of white balls after a number of draws, and determine the structure of the moments. Moreover, we obtain a strong law of large numbers, and a central limit theorem for the number of white balls. Interestingly, the central limit theorem is obtained combinatorially via the method of moments and probabilistically via martingales. We briefly discuss the merits of each approach. The connection to a few other related urn models is briefly sketched. 相似文献
9.
The exact and the asymptotic non-null distribution of the maximal invariant corresponding to testing that the covariance matrix of a 2m-dimensional real normal distribution has complex structure is obtained. 相似文献
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U. B. Singh 《Proceedings Mathematical Sciences》1995,105(1):41-51
During the last five decades, a number of combinatorial generalizations and interpretations have occurred for the identities
of the Rogers-Ramanujan type. The object of this paper is to give a most general known analytic auxiliary functional generalization
which can be used to give combinatorial interpretations of generalizedq-identities of the Rogers-Ramanujan type. The derivation realise the theory of basic hypergeometric series with two unconnected
bases. 相似文献
12.
Let the column vectors of X:: M×N, M<N, be distributed as independent complex normal vectors with the same covariance matrix Σ. Then the usual quadratic form in the complex normal vectors is denoted by Z=XLXH where L: N×N is a positive definite hermitian matrix. This paper deals with a representation for the density function of Z in terms of a ratio of determinants. This representation also yields a compact form for the distribution of the generalized variance |Z|. 相似文献
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THE EXISTENCE OF MOMENTS OF NONLINEAR AUTOREGRESSIVE MODEL 总被引:2,自引:0,他引:2
1.IntroductionConsiderthefollowingnonlinearautoregressivemodelwhere{E,}isasequenceofindependentidenticallydistributedrandomvariableswithacommonalmosteverywherepositivedensityandfinitefirstmoment.stisindependentofat--s)s21.op')isameasurablefunctionfromRP-- RI.Writewhere"T"standsfortransposeofamatrixoravector.Then(1)canberewritteninthevectorformX,=T(Xt--l) et'(2)Sinceweneedthestrictstationarity,ergodicityandtheexistenceofcertainmomentsintheestimationtheoryoftimeseries,thegeometricalergodicit… 相似文献
14.
We derive a formula for the n-row Macdonald polynomials with the coefficients presented both combinatorically and in terms of very-well-poised hypergeometric series. 相似文献
15.
This article is a survey on recent studies on special solutions of the discrete Painlevé equations, especially on hypergeometric solutions of the q-Painlevé equations. The main part of this survey is based on the joint work [K. Kajiwara, T. Masuda, M. Noumi, Y. Ohta, Y. Yamada, Hypergeometric solutions to the q-Painlevé equations, IMRN 2004 47 (2004) 2497–2521, K. Kajiwara, T. Masuda, M. Noumi, Y. Ohta, Y. Yamada, Construction of hypergeometric solutions to the q-Painlevé equations, IMRN 2005 24 (2005) 1439–1463] with Kajiwara, Masuda, Ohta and Yamada. After recalling some basic facts concerning Painlevé equations for comparison, we give an overview of the present status of studies on difference (discrete) Painlevé equations as a source of special functions. 相似文献
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陈伟 《数学的实践与认识》2004,34(6):155-158
将 C.Krattenthaler的矩阵反演恰当地用于初文昌的恒等式得到了 F.H.Jackson的超几何级数公式 87的推广 . 相似文献
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BAI Peng Department of Statistics University of Yunnan Kunming China 《中国科学A辑(英文版)》2005,48(12):1597-1608
For a GMANOVA-MANOVA model with normal error: Y = XB1Z1 T B2Z2 T E, E- Nq×n(0, In (?) ∑), the present paper is devoted to the study of distribution of MLE, ∑, of covariance matrix ∑. The main results obtained are stated as follows: (1) When rk(Z) -rk(Z2) ≥ q-rk(X), the exact distribution of ∑ is derived, where z = (Z1,Z2), rk(A) denotes the rank of matrix A. (2) The exact distribution of |∑| is gained. (3) It is proved that ntr{[S-1 - ∑-1XM(MTXT∑-1XM)-1MTXT∑-1]∑}has X2(q_rk(x))(n-rk(z2)) distribution, where M is the matrix whose columns are the standardized orthogonal eigenvectors corresponding to the nonzero eigenvalues of XT∑-1X. 相似文献
18.
In this paper, we study of Pólya urn model containing balls of (m+1) different labels under a general replacement scheme, which is characterized by an (m+1) × (m+1) addition matrix of integers without constraints on the values of these (m+1)2 integers other than non-negativity. LetX
1,X
2,...,X
n
be trials obtained by the Pólya urn scheme (with possible outcomes: “O”, “1”,...“m”). We consider the multivariate distributions of the numbers of occurrences of runs of different types arising from the various
enumeration schemes and give a recursive formula of the probability generating function. Some closed form expressions are
derived as special cases, which have potential applications to various areas. Our methods for the derivation of the multivariate
run-related distribution are very simple and suitable for numerical and symbolic calculations by means of computer algebra
systems. The results presented here develop a general workable framework for the study of Pólya urn models. Our attempts are
very useful for understanding non-classic urn models. Finally, numerical examples are also given in order to illustrate the
feasibility of our results.
This research was partially supported by the ISM Cooperative Research Program (2003-ISM·CRP-2007). 相似文献
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研究了非还原取样模型中负超几何随机变量的联合分布,得到了若干有用的推论.据此给出了负超几何分布的期望和方差的一种分解算法. 相似文献
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This paper provides computable representations for the evaluation of the probability content of cones in isotropic random fields. A decomposition of quadratic forms in spherically symmetric random vectors is obtained and a representation of their moments is derived in terms of finite sums. These results are combined to obtain the distribution function of quadratic forms in spherically symmetric or central elliptically contoured random vectors. Some numerical examples involving the sample serial covariance are provided. Ratios of quadratic forms are also discussed. 相似文献