Multivariate Discrete Distributions with a Product-Type Dependence

A discrete multivariate probability distribution for dependent random variables, which contains the Poisson and Geometric conditionals distributions as particular cases, is characterized by means of conditional expectations of arbitrary one-to-one functions. Independence of the random variables is also characterized in terms of these conditional expectations. For certain exchangeable and partially exchangeable random variables with a joint distribution of this form it is shown that maximum likelihood estimates coincide with the simple method of moments estimates, suggesting that these models offer a pragmatic way to analyze certain dependent data.     

On the product of symmetric random variables

Let X and Y be two independent and nondegenerate random variables such that X is symmetric about a and Y is symmetric about b. It is shown that XY is symmetric about ab if and only if ab= 0.     

离散型随机变量的几种独立性及相互关系

随机变量的独立性在概率论中有着十分重要的意义.本文给出了离散型随机变量与离散型随机向量相互独立的概念,条件独立的概念,以及几种独立性的相互关系.     

Construction of multivariate distributions with given marginals

Summary We make some remarks on the problem how to construct probability measures with given marginals. Questions of this kind arise if one wants to build a stochastic model in a situation where one has some idea of the kind of dependence and knows exactly certain marginal distributions.     

Waiting Time Distributions Associated with Runs of Fixed Length in Two-State Markov Chains

In the present article a general technique is developed for the evaluation of the exact distribution in a wide class of waiting time problems. As an application the waiting time for the r-th appearance of success runs of specified length in a sequence of outcomes evolving from a first order two-state Markov chain is systematically investigated and asymptotic results are established. Several extensions and generalisations are also discussed.     

小波分析在测试信号分析中的应用

本文给出了小波的基本原理和构造方法以及小波分析的快速算法,将小波分析方法（ＷＡＭ）引入到非平稳冲击信号的分析中,作为小波分析应用实例,对汽车齿轮箱的断齿测信号进行了分析,给出了分析结果     

多个离散分布的信息差度量的渐近分布

本文中对于多信息源的信息差异性度量B,我们研究了B(u1,u2,…,us)的渐近分布,其中u1,u2,…us是某个概率分布的样本估计．在某些较弱的条件下,我们证明了nB(u1,u2,…,us)的极限分布是自由度为1的X2分布的加权和,其中n是样本容量,u1,u2,…,us不必相互独立．     

附加广义函数的一般形式

作者证明了两两次数不同的附加广义函数组的线性无关性，接着给出了附加广义函数的一般形式。     

Decompounding poisson random sums: Recursively truncated estimates in the discrete case

Given a sample from a discrete compound Poisson distribution, we consider variants of plug-in and likelihood estimators for the corresponding base distribution. These proceed recursively with an intermediate truncation step. We discuss the asymptotic behaviour of the estimators and give some numerical examples. Both procedures compare favourably with the straightforward and the naively projected plug-in estimator that we introduced in Buchmann and Grübel (2003,The Annals of Statistics,31, 1054–1074).     

An algebraic approach to tempered distributions

A space of pseudoquotients is introduced that is shown to be isomorphic to the space of tempered distributions on RN. The Fourier transform is defined as a map from the space of pseudoquotients to the space of tempered distributions and as a transformation on pseudoquotients.     

The lower bound on independence number

Let G be a graph with degree sequence ( d_v). If the maximum degree of any subgraph induced by a neighborhood of G is at most m, then the independence number of G is at least , where f_m+1( x) is a function greater than for x> 0. For a weighted graph G = ( V, E, w), we prove that its weighted independence number (the maximum sum of the weights of an independent set in G) is at least where w_v is the weight of v.     

Independent Sets in Graph Powers are Almost Contained in Juntas

Let G = (V,E) be a simple undirected graph. Define G ⁿ , the n-th power of G, as the graph on the vertex set V ⁿ in which two vertices (u ₁, . . . , u _n ) and (v ₁, . . . , v _n ) are adjacent if and only if u _i is adjacent to v _i in G for every i. We give a characterization of all independent sets in such graphs whenever G is connected and non-bipartite. Consider the stationary measure of the simple random walk on G ⁿ . We show that every independent set is almost contained with respect to this measure in a junta, a cylinder of constant co-dimension. Moreover we show that the projection of that junta defines a nearly independent set, i.e. it spans few edges (this also guarantees that it is not trivially the entire vertex-set). Our approach is based on an analog of Fourier analysis for product spaces combined with spectral techniques and on a powerful invariance principle presented in [MoOO]. This principle has already been shown in [DiMR] to imply that independent sets in such graph products have an influential coordinate. In this work we prove that in fact there is a set of few coordinates and a junta on them that capture the independent set almost completely. I.D. is the incumbent of the Harry and Abe Sherman Lectureship Chair at Hebrew Univeristy. Her research is supported by the Israel Science Foundation and by the Binational Science Foundation. E.F.’s research is supported in part by the Israel Science Foundation, grant no. 0329745. O.R. is supported by an Alon Fellowship, by the Binational Science Foundation, by the Israel Science Foundation, and by the European Commission under the Integrated Project QAP funded by the IST directorate as Contract Number 015848.