共查询到20条相似文献,搜索用时 31 毫秒
1.
本文在比较一般的条件下得到了平稳NA序列的中偏差下界估计,进而得到平稳NA序列的中偏差原理。 相似文献
2.
A. I. Sakhanenko 《Siberian Mathematical Journal》2011,52(4):696-710
We obtain estimates for the accuracy with which a random broken line constructed from sums of independent nonidentically distributed
random variables can be approximated by a Wiener process. All estimates depend explicitly on the moments of the random variables;
meanwhile, these moments can be of a rather general form. In the case of identically distributed random variables we succeed
for the first time in constructing an estimate depending explicitly on the common distribution of the summands and directly
implying all results of the famous articles by Komlós, Major, and Tusnády which are devoted to estimates in the invariance
principle. 相似文献
3.
In this paper, we obtain sample path and scalar large deviation principles for the product of sums of positive random variables. We study the case when the positive random variables are independent and identically distributed and bounded away from zero or the left tail decays to zero sufficiently fast. The explicit formula for the rate function of a scalar large deviation principle is given in the case when random variables are exponentially distributed. 相似文献
4.
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. 相似文献
5.
A. A. Borovkov 《Siberian Advances in Mathematics》2016,26(4):231-246
In Section 1, we prove stability theorems for a series of boundary functionals of random walks. In Section 2, we suggest a new simpler proof of the theorem on threshold phenomena for the distribution of the maximum of the consecutive sums of random variables. In Section 3, we find the second-order asymptotics for this distribution under the assumption that the third moments of the random variables exist. 相似文献
6.
7.
利用分析方法建立了用不等式表示的用渐近平均对数似然比刻划的服从二项分布的随机变量序列的强偏差定理,作为推论得到了服从二项分布的相依随机变量序列的强大数定律. 相似文献
8.
Zinoviy Landsman 《Statistics & probability letters》2011,81(3):382-391
Rogers and Shi (1995) have used the technique of conditional expectations to derive approximations for the distribution of a sum of lognormals. In this paper we extend their results to more general sums of random variables. In particular we study sums of functions of dependent random variables that are multivariate normally distributed and also derive results for sums of functions of dependent random variables from the additive exponential dispersion family. The usefulness of our results for practical applications is also discussed. 相似文献
9.
《中国科学 数学(英文版)》2015,(6)
We obtain a general invariance principle of G-Brownian motion for the law of the iterated logarithm(LIL for short). For continuous bounded independent and identically distributed random variables in G-expectation space, we also give an invariance principle for LIL. In some sense, this result is an extension of the classical Strassen's invariance principle to the case where probability measure is no longer additive. Furthermore,we give some examples as applications. 相似文献
10.
11.
A Heuristic for Moment-Matching Scenario Generation 总被引:1,自引:0,他引:1
Kjetil Høyland Michal Kaut Stein W. Wallace 《Computational Optimization and Applications》2003,24(2-3):169-185
In stochastic programming models we always face the problem of how to represent the random variables. This is particularly difficult with multidimensional distributions. We present an algorithm that produces a discrete joint distribution consistent with specified values of the first four marginal moments and correlations. The joint distribution is constructed by decomposing the multivariate problem into univariate ones, and using an iterative procedure that combines simulation, Cholesky decomposition and various transformations to achieve the correct correlations without changing the marginal moments.With the algorithm, we can generate 1000 one-period scenarios for 12 random variables in 16 seconds, and for 20 random variables in 48 seconds, on a Pentium III machine. 相似文献
12.
In this paper we study the behavior of concentration functions of weighted sums of independent random variables with respect to the arithmetic structure of coefficients. Recently, Tao and Vu formulated a so-called Inverse Principle in the Littlewood–Offord problem. We discuss the relations between this Inverse Principle and a similar principle formulated for sums of arbitrarily distributed independent random variables formulated by T. Arak in the 1980’s. 相似文献
13.
本文利用鞅的Skorohod表示, 在序列是高斯的且序列的协方差系数以幂指数速度递减的条件下,证明了相伴高斯随机变量序列的一个强不变原理\bd 作为推论得到了相伴高斯随机变量序列的重对数律和钟重对数律 相似文献
14.
In this article, we derive the distribution of partially exchangeable binary random variables, generalizing the distribution of exchangeable binary random variables and hence the binomial distribution. The distribution can be viewed as a mixture of Markov chains. We introduce rectangular complete monotonicity and show that partial exchangebility can be characterized by rectangular complete monotonicity. The distribution aided with rectangular complete monotonicity can be used to analyze serially correlated data common in many areas of science. 相似文献
15.
David M. Bradley Ramesh C. Gupta 《Annals of the Institute of Statistical Mathematics》2002,54(3):689-700
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. 相似文献
16.
Ascending Runs in Dependent Uniformly Distributed Random Variables: Application to Wireless Networks
Nathalie Mitton Katy Paroux Bruno Sericola Sébastien Tixeuil 《Methodology and Computing in Applied Probability》2010,12(1):51-62
We analyze in this paper the longest increasing contiguous sequence or maximal ascending run of random variables with common
uniform distribution but not independent. Their dependence is characterized by the fact that two successive random variables
cannot take the same value. Using a Markov chain approach, we study the distribution of the maximal ascending run and we develop
an algorithm to compute it. This problem comes from the analysis of several self-organizing protocols designed for large-scale
wireless sensor networks, and we show how our results apply to this domain. 相似文献
17.
In this paper we formulate and prove a general principle which enables us to deduce limit theorems for a sequence of random variables on a finitely additive probability space. 相似文献
18.
On the exact distribution of linear combinations of order statistics from dependent random variables 总被引:2,自引:0,他引:2
We study the exact distribution of linear combinations of order statistics of arbitrary (absolutely continuous) dependent random variables. In particular, we examine the case where the random variables have a joint elliptically contoured distribution and the case where the random variables are exchangeable. We investigate also the particular L-statistics that simply yield a set of order statistics, and study their joint distribution. We present the application of our results to genetic selection problems, design of cellular phone receivers, and visual acuity. We give illustrative examples based on the multivariate normal and multivariate Student t distributions. 相似文献
19.
Ka Chun Cheung 《Insurance: Mathematics and Economics》2010,47(2):130-136
In this article, we characterize comonotonicity and related dependence structures among several random variables by the distribution of their sum. First we prove that if the sum has the same distribution as the corresponding comonotonic sum, then the underlying random variables must be comonotonic as long as each of them is integrable. In the literature, this result is only known to be true if either each random variable is square integrable or possesses a continuous distribution function. We then study the situation when the distribution of the sum only coincides with the corresponding comonotonic sum in the tail. This leads to the dependence structure known as tail comonotonicity. Finally, by establishing some new results concerning convex order, we show that comonotonicity can also be characterized by expected utility and distortion risk measures. 相似文献
20.
Sigeo Aki 《Annals of the Institute of Statistical Mathematics》2012,64(3):633-655
This paper proposes a new method for constructing a sequence of infinitely exchangeable uniform random variables on the unit
interval. For constructing the sequence, we utilize a Pólya urn partially. The resulting exchangeable sequence depends on
the initial numbers of balls of the Pólya urn. We also derive the de Finetti measure for the exchangeable sequence. For an
arbitrarily given one-dimensional distribution function, we generate sequences of exchangeable random variables with the one-dimensional
marginal distribution by transforming the exchangeable uniform sequences with the inverse function of the distribution function.
Among them we mainly investigate sequences of exchangeable discrete random variables. They differ from the well-known exchangeable
sequence generated only by the Pólya urn scheme. Some examples are also given as applications of the results to exact distributions
of some statistics based on sequences of exchangeable trials. Further, from the above exchangeable uniform sequence we construct
partial or Markov exchangeable sequences. We also provide numerical examples of statistical inference based on the exchangeable
and Markov exchangeable sequences. 相似文献