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1.
R. -D. Reiss 《Annals of the Institute of Statistical Mathematics》1985,37(1):529-533
Summary In the present note we give short proofs of asymptotic theorems for the distributions of extreme and intermediate ordered
distance random variables. Moreover, a quick goodness-of-fit test is proposed which is based on a single intermediate ordered
distance random variable. 相似文献
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V. N. Sudakov 《Journal of Mathematical Sciences》1998,88(1):106-109
The existence of typical distributions for random variables chosen at random from a finite-dimensional random variable vector
space of high dimension is established. Possible typical distributions are described, and conditions for the typical distribution
to be standard Gaussian are given. Bibliography: 2 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 216, 1994, pp. 153–160.
Translated by the author. 相似文献
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M. Vlyushina 《Journal of Mathematical Sciences》1996,78(1):115-124
We consider the following problem: for what polynomials P and Q does the equality
imply
, the common distribution F of discrete random variables X1 and X2 being given.
Proceedings of the XVI Seminar on Stability Problems for Stochastic Models, Part II, Eger. Hungary, 1994 相似文献
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Gregory Beylkin Lucas Monzón Ignas Satkauskas 《Applied and Computational Harmonic Analysis》2019,46(2):400-416
We introduce a new functional representation of probability density functions (PDFs) of non-negative random variables via a product of a monomial factor and linear combinations of decaying exponentials with complex exponents. This approximate representation of PDFs is obtained for any finite, user-selected accuracy. Using a fast algorithm involving Hankel matrices, we develop a general numerical method for computing the PDF of the sums, products, or quotients of any number of non-negative independent random variables yielding the result in the same type of functional representation. We present several examples to demonstrate the accuracy of the approach. 相似文献
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Petr Savický 《Random Structures and Algorithms》2000,16(3):233-239
Ordered binary decision diagrams (OBDDs) are a model for representing Boolean functions. There is also a more powerful variant called parity OBDDs. The size of the representation of a given function depends in both these models on the chosen ordering of the variables. It is known that there are functions such that almost all orderings of their variables yield an OBDD of polynomial size, but there are also some exceptional orderings, for which the size is exponential. We prove that for parity OBDDs, the size for a random ordering and the size for the worst ordering are polynomially related. More exactly, for every ϵ>0 there is a number c>0 such that the following holds. If a Boolean function f of n variables is such that a random ordering of the variables yields a parity OBDD for f of size at most s with probability at least ϵ, where s≥n, then every ordering of the variables yields a parity OBDD for f of size at most sc. © 2000 John Wiley & Sons, Inc. Random Struct. Alg., 16: 233–239, 2000 相似文献
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We consider tuples {N jk }, j = 1, 2, ..., k = 1, ..., q j , of nonnegative integers such that $$ \sum\limits_{j = 1}^\infty {\sum\limits_{k = 1}^{q_j } {jN_{jk} } } \leqslant M. $$ Assuming that q j ~ j d?1, 1 < d < 2, we study how the probabilities of deviations of the sums $ \sum\nolimits_{j = j_1 }^{j_2 } {\sum\nolimits_{k = 1}^{q_j } {N_{jk} } } $ N jk from the corresponding integrals of the Bose-Einstein distribution depend on the choice of the interval [j 1,j 2]. 相似文献
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We consider the mathematical problem of the allocation of indistinguishable particles to integer energy levels under the condition that the number of particles can be arbitrary and the total energy of the system is bounded above. Systems of integer as well as fractional dimension are considered. The occupation numbers can either be arbitrary nonnegative integers (the case of “Bose particles”) or lie in a finite set {0, 1, …, R} (the case of so-called parastatistics; for example, R = 1 corresponds to the Fermi-Dirac statistics). Assuming that all allocations satisfying the given constraints are equiprobable, we study the phenomenon whereby, for large energies, most of the allocations tend to concentrate near the limit distribution corresponding to the given parastatistics. 相似文献
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We continue our study of the problem on the allocation of indistinguishable particles to integer energy levels under the condition that the total energy of the system is bounded above. It is shown that the Bose condensation phenomenon can occur in this model. Systems of dimension d < 1 (including negative dimensions) are studied. 相似文献
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Sergio Albeverio Yana Gontcharenko Mykola Pratsiovytyi Grygoriy Torbin 《Mathematische Nachrichten》2006,279(15):1619-1633
Formulas are given for the Lebesgue measure and the Hausdorff–Besicovitch dimension of the minimal closed set Sξ supporting the distribution of the random variable ξ = 2–k τk, where τk are independent random variables taking the values 0, 1, 2 with probabilities p 0k , p 1k , p 2k , respectively. A classification of the distributions of the r.v. ξ via the metric‐topological properties of Sξ is given. Necessary and sufficient conditions for superfractality and anomalous fractality of Sξ are found. It is also proven that for any real number a 0 ∈ [0, 1] there exists a distribution of the r.v. ξ such that the Hausdorff–Besicovitch dimension of Sξ is equal to a 0. The results are applied to the study of the metric‐topological properties of the convolutions of random variables with independent binary digits, i.e., random variables ξi = , where ηk are independent random variables taking the values 0 and 1. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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A. Aksomaitis 《Lithuanian Mathematical Journal》1990,30(2):87-96
Kaunas Polytechnic Institute. Translated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 30, No. 2, pp. 219–232, April–June, 1990. 相似文献