共查询到20条相似文献,搜索用时 9 毫秒
1.
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
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The distribution of a sum S of independent binomial random variables, each with different success probabilities, is discussed. An efficient algorithm is given to calculate the exact distribution by convolution. Two approximations are examined, one based on a method of Kolmogorov, and another based on fitting a distribution from the Pearson family. The Kolmogorov approximation is given as an algorithm, with a worked example. The Kolmogorov and Pearson approximations are compared for several given sets of binomials with different sample sizes and probabilities. Other methods of approximation are discussed and some compared numerically. The Kolmogorov approximation is found to be extremely accurate, and the Pearson curve approximation useful if extreme accuracy is not required. 相似文献
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Dominik Kortschak Hansjörg Albrecher 《Methodology and Computing in Applied Probability》2009,11(3):279-306
In this paper we extend some results about the probability that the sum of n dependent subexponential random variables exceeds a given threshold u. In particular, the case of non-identically distributed and not necessarily positive random variables is investigated. Furthermore
we establish criteria how far the tail of the marginal distribution of an individual summand may deviate from the others so
that it still influences the asymptotic behavior of the sum. Finally we explicitly construct a dependence structure for which,
even for regularly varying marginal distributions, no asymptotic limit of the tail of the sum exists. Some explicit calculations
for diagonal copulas and t-copulas are given.
Dominik Kortschak was supported by the Austrian Science Fund Project P18392. 相似文献
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Doklady Mathematics - Given a sum of a finite number of independent random variables, the asymptotic behavior of its distributions and densities at infinity is investigated in the case when the... 相似文献
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介绍了一个在计算机科学、信息科学等学科中具有广泛应用的随机变量和的模函数,计算了其分布,并提供了该函数在图像信息安全领域的一个应用例子,验证了理论结果. 相似文献
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关于DRCE随机变量渐近分布性质的探讨 总被引:1,自引:0,他引:1
本文讨论了DRCE随机变量渐近正态收敛速度的一致上、下界,并对一类特殊的DRCE随机变量,讨论了其退化情况的不变原理。 相似文献
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This article deals with probability distributions of sums of simple random sample and Bernoulli sample when samples are selected from finite population of independent random variables. Random variables are quasi-lattice. Probability distributions from class ? and Poisson distribution are used for approximation. Analogue of Cornish-Fisher transformation is obtained in case of limit distributions from class ?. 相似文献
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Mukhopadhyay Nitis Bapat Sudeep R. 《Methodology and Computing in Applied Probability》2019,21(3):853-873
Methodology and Computing in Applied Probability - Butler and Stephens (2017) have investigated the exact and approximate distributions of a sum S of independent binomial random variables with... 相似文献
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Christopher R. Dance 《Journal of Theoretical Probability》2014,27(2):358-369
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. 相似文献
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Let X1, ... , Xn be i.i.d. integral valued random variables and Sn their sum. In the case when X1 has a moderately large tail of distribution, Deshouillers, Freiman and Yudin gave a uniform upper bound for max k ∊ ℤ Pr{Sn = k} (which can be expressed in term of the Lévy Doeblin concentration of Sn), under the extra condition that X1 is not essentially supported by an arithmetic progression. The first aim of the paper is to show that this extra condition cannot be simply ruled out. Secondly, it is shown that if X1 has a very large tail (larger than a Cauchy-type distribution), then the extra arithmetic condition is not sufficient to guarantee a uniform upper bound for the decay of the concentration of the sum Sn. Proofs are constructive and enhance the connection between additive number theory and probability theory.À Jean-Louis Nicolas, avec amitié et respect2000 Mathematics Subject Classification: Primary—60Fxx, 60Exx, 11Pxx, 11B25 相似文献
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设t0∈(0,1),Wni(t0)是关于实变量t1,t2,…,tn的权函数;随机变量序列Y1,Y2,…,Yn,iid.本研究了随机变量序列加权和∑(i=1,n)Wni(t0)Yi的相合性. 相似文献
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本文讨论了双向无穷B-值随机变量序列加权和的弱大数定律、Lr收敛性、完全收敛性.并由此刻画了空间的几何性质. 相似文献
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John Baxter Roger Jones Michael Lin James Olsen 《Journal of Theoretical Probability》2004,17(1):165-181
For any sequence {a
k
} with sup
for some q>1, we prove that
converges to 0 a.s. for every {X
n
} i.i.d. with E(|X
1|)< and E(X
1)=0; the result is no longer true for q=1, not even for the class of i.i.d. with X
1 bounded. We also show that if {a
k
} is a typical output of a strictly stationary sequence with finite absolute first moment, then for every i.i.d. sequence {X
n
{ with finite absolute pth moment for some p> 1,
converges a.s. 相似文献
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Mohsen Soltanifar 《Journal of Theoretical Probability》2014,27(1):41-56
In this paper, we discuss some special properties of operator-valued semicircular random variables including representation of the Cauchy transform of a compactly supported probability measure in terms of their operator-valued Cauchy transforms and existence of nonzero discrete part of their associated distributions. 相似文献
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The work is designated for obtaining asymptotic expansions and determination of structures of the remainder terms that take into consideration large deviations both in the Cramer zone and Linnik power zones for the distribution density function of sums of independent random variables in a triangular array scheme. The result was obtained using general Lemma 6.1 of Saulis and Statuleviius in Limit Theorems for Large Deviations (Kluwer, 1991) and joining the methods of characteristic functions and cumulants. The work extends the theory of sums of random variables and in a special case, improves S. A.Book's results on sums of random variables with weights. 相似文献
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On the Subexponential Property of a Class of Random Variables 总被引:1,自引:0,他引:1
Mathematical Notes - 相似文献