B值行独立随机元阵列的矩完全收敛性

本文研究了B值行独立的随机元阵列的矩完全收敛性.利用B值行独立的随机元阵列的概率不等式,在随机元阵列随机有界于某非负随机变量的条件下,获得了B值行独立的随机元阵列的矩完全收敛性的一些充分条件,并完善了Chow关于实值独立同分布随机变量列的矩完全收敛性的结果.     

B值随机元阵列矩完全收敛性的进一步讨论

完全收敛性是概率极限理论中的一个重要的概念.考虑了矩完全收敛性,在随机元阵列随机有界于某非负随机变量的条件下,通过引入函数类S,得到了B值行独立对称的随机元阵列矩完全收敛性的一些充分条件.同时得到了p型Banach空间中独立零均值随机元序列矩完全收敛性的一个充分条件.     

二维连续型随机变量相互独立的一个充分条件

提出了一个有关二维连续型随机变量相互独立的充分条件.该条件表明,如果二维连续型随机变量在任意概率值非0的矩形区域上被标准化后满足乘积的数学期望等于数学期望的乘积,则可推出它们是相互独立的.     

对数似然比与整值随机变量序列的一类强律

本文引进对数似然比作为整值随机变量序列相对于服从几何分布的独立随机变量序列的偏差的一种度量,并通过限制对数似然比给出了样本空间的一个子集.在此子集上得到了一类用不等式表示的强律,其中包含整值随机变量序列与相对熵密度及几何分布的熵函数有关的若干极限性质.     

逆Weibull分布随机变量的随机比较

研究了两个相互独立的逆Weibull分布随机变量间的随机序,似然比序,危险率序以及凸序之间的相互关系,给出了两个相互独立但不同分布的随机变量满足各种随机序时其分布所含参数间的相应关系．也给出了两组相互独立但不同分布的随机变量极值间在一般随机序下的大小关系．     

逆Weibull分布随机变量的随机比较(英文)

研究了两个相互独立的逆Weibull分布随机变量间的随机序,似然比序,危险率序以及凸序之间的相互关系,给出了两个相互独立但不同分布的随机变量满足各种随机序时其分布所含参数间的相应关系.也给出了两组相互独立但不同分布的随机变量极值间在一般随机序下的大小关系.     

行为ND随机变量阵列加权和的完全收敛性

在非同分布的情况下,给出了行为ND随机变量阵列加权和的完全收敛性的充分条件,所得结果部分地推广了独立随机变量和NA随机变量的相应结果.作为其应用,获得了ND随机变量序列加权和的Marcinkiewicz-Zygmund型强大数定律.     

B值随机变量序列的局部收敛定理

本文的目的是研究B值随机变量序列的局部收敛定理。作为推论，得到了一类B值鞅差序列的极限定理和若干经典的独立随机变量序列的极限定理。     

Ⅰ型极值分布随机变量的随机比较

研究了两个相互独立的Ⅰ型极大值分布随机变量间的随机序,似然比序,危险率序及凸序之间的相互关系,给出了两个相互独立但不同分布的随机变量满足各种随机序时其分布所含参数间的相应关系．文中也给出了两组相互独立但不同分布的随机变量极值间在一般随机序下的大小关系．     

Ⅰ型极值分布随机变量的随机比较(英文)

研究了两个相互独立的Ⅰ型极大值分布随机变量间的随机序,似然比序,危险率序及凸序之间的相互关系,给出了两个相互独立但不同分布的随机变量满足各种随机序时其分布所含参数间的相应关系.文中也给出了两组相互独立但不同分布的随机变量极值间在一般随机序下的大小关系.     

On the Distribution of the Sum of n Non-Identically Distributed Uniform Random Variables

The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the characteristic function, we derive explicit formulae for the distribution of the sum of n non-identically distributed uniform random variables in both the continuous and the discrete case. The results, though involved, have a certain elegance. As examples, we derive from our general formulae some special cases which have appeared in the literature.     

Some Asymptotic Results for One-Sided Large Deviation Probabilities

We investigate the asymptotic behavior of the sum of independent real random variables. We assume that the random variables are not identically distributed but the average of distribution functions of these random variables is equivalent to some heavy-tailed limit distribution function. An example with Pareto law as limit function is given.     

Series representations for densities functions of a family of distributions—Application to sums of independent random variables

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.     

On the probabilistic analysis of an approximation algorithm for solving the <Emphasis Type="Italic">p</Emphasis>-median problem

In order to solve the location problem in the p-median form we present an approximation algorithm with time complexity O(n ₂) and the results of its probabilistic analysis. The input data are defined on a complete graph with distances between the vertices expressed by the independent random variables with the same uniform distribution. The value of the objective function produced by the algorithm amounts to a certain sum of the random variables that we analyze basing on an estimate for the probabilities of large deviations of these sums. We use a limit theorem in the form of the Petrov inequalities, taking into account the dependence of the random variables in the sum. The probabilistic analysis yields some estimates for the relative error and the failure probability of our algorithm, as well as conditions for its asymptotic exactness.     

An elementary proof of the local central limit theorem

We give an elementary proof of the local central limit theorem for independent, non-identically distributed, integer valued and vector valued random variables.Support by a NSF Grant.Supported by an NSERC Grant     

On the Distribution of Sums of Independent Exponential Random Variables Via Wilks’ Integral Representation

In this note we consider an alternative approach to compute the distribution of the sum of independent exponential random variables. In particular, by considering the logarithmic relation between exponential and beta distribution functions and by considering the Wilks’ integral representation for the product of independent beta random variables, we provide a closed-form expression for the distribution of the sum of independent exponential random variables. The expression we obtain is simpler than the ones previously obtained in the literature.     

Asymptotic properties of digit sequences of random numbers

We consider several aspects of the relationship between a [0, 1]‐valued random variable X and the random sequence of digits given by its m‐ary expansion. We present results for three cases: (a) independent and identically distributed digit sequences; (b) random variables X with smooth densities; (c) stationary digit sequences. In the case of i.i.d. an integral limit thorem is proved which applies for example to relative frequencies, yielding asymptotic moment identities. We deal with occurrence probabilities of digit groups in the case that X has an analytic Lebesgue density. In the case of stationary digits we determine the distribution of X in terms of their transition functions. We study an associated [0, 1]‐valued Markov chain, in particular its ergodicity, and give conditions for the existence of stationary digit sequences with prespecified transition functions. It is shown that all probability measures induced on [0, 1] by such sequences are purely singular except for the uniform distribution. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

An Inequality for the Sum of Independent Bounded Random Variables

We give a simple inequality for the sum of independent, bounded random variables. This inequality improves on the celebrated result of Hoeffding in a special case. It is optimal in the limit where the sum tends to a Poisson random variable.     

渐近正态随机变量函数的极限分布

基于渐近正态随机变量,导出随机变量函数极限分布的两个一般性理论结果.作为应用,证明了渐近正态随机变量一系列具体函数的极限分布,其中包括泊松随机变量平方根的渐近正态性,以及随机变量部分和在正则化常数是随机变量情况下的渐近正态性.     

On Elliptic Problems in Besov Spaces

Suppose that the distribution function of a standardized sum of independent identically distributed random variables tends to a stable law as n°. Some differences in moments and pseudomoments, inequalities of the BERRY-ESSEEN-Type and asymptotic expansions are characterized when the limit law is either normal or non-normal stable.