共查询到20条相似文献,搜索用时 11 毫秒
1.
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
2.
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
3.
We provide precise bounds for tail probabilities, say {M
n
x}, of sums M
n
of bounded i.i.d. random variables. The bounds are expressed through tail probabilities of sums of i.i.d. Bernoulli random variables. In other words, we show that the tails are sub-Bernoullian. Sub-Bernoullian tails are dominated by Gaussian tails. Possible extensions of the methods are discussed. 相似文献
4.
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
5.
L. V. Rozovsky 《Journal of Mathematical Sciences》2002,109(6):2192-2209
The goal of this paper is to obtain nonasymptotic estimates from below for large deviation probabilities of a sum of independent random variables that generalize, refine, and are more natural than analogous estimates of other authors. Bibliography: 14 titles. 相似文献
6.
Let {X
1,...,X
N} be a set of N independent random variables, and let S
n
be a sum of n random variables chosen without replacement from the set {X
1,...,X
N} with equal probabilities. In this paper we give an estimate of the remainder term for the normal approximation of S
n
under mild conditions. 相似文献
7.
8.
讨论了两两独立随机变量列加权和在满足r(1≤r<2)阶Ces`aro一致可积条件下的Lr收敛性,获得了与独立情形一致的结果.用相似的方法,对于其它相依或混合序列(如两两NQD列,φ-混合序列,ρ-混合序列)也有相同的结果. 相似文献
9.
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
10.
Pieter C. Allaart 《随机分析与应用》2013,31(3):531-554
Abstract Let X 1, X 2,… be any sequence of [0,1]-valued random variables. A complete comparison is made between the expected maximum E(max j≤n Y j ) and the stop rule supremum sup t E Y t for two types of discounted sequences: (i) Y j = b j X j , where {b j } is a nonincreasing sequence of positive numbers with b 1 = 1; and (ii) Y j = B 1… B j?1 X j , where B 1, B 2,… are independent [0,1]-valued random variables that are independent of the X j , having a common mean β. For instance, it is shown that the set of points {(x, y): x = sup t E Y {(x, y): x=sup t E Y and y = E(max j≤n Y j ), for some sequence X 1,…,X n and Y j = b j X j }, is precisely the convex closure of the union of the sets {(b j x, b j y): (x, y) ∈ C j }, j = 1,…,n, where C j = {(x, y):0 ≤ x ≤ 1, x ≤ y ≤ x[1 + (j ? 1)(1 ? x 1/(j?1))]} is the prophet region for undiscounted random variables given by Hill and Kertz [8]. As a special case, it is shown that the maximum possible difference E(max j≤n β j?1 X j ) ? sup t E(β t?1 X t ) is attained by independent random variables when β ≤ 27/32, but by a martingale-like sequence when β > 27/32. Prophet regions for infinite sequences are given also. 相似文献
11.
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
12.
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
13.
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
14.
We investigate random variables in Lorentz spaces Lp,q. Conditionson the characteristic function are obtained which imply thata random variable belongs to the Lorentz space. Using them,we prove some estimates for the Lp,q-norm of sums of independentrandom variables. Some of these estimates are new for the spacesLp. 相似文献
15.
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
16.
Lithuanian Mathematical Journal - In this paper, we generalize a result on approximation of sums by sums with a fixed number of summands in [V. Bentkus, A new method for approximation in... 相似文献
17.
Ramesh M. Korwar 《Journal of multivariate analysis》2002,80(2):344
In this paper, it is shown that a convolution of uniform distributions (a) is more dispersed and (b) has a smaller hazard rate when the scale parameters of the uniform distributions are more dispersed in the sense of majorization. It is also shown that a convolution of gamma distributions with a common shape parameter greater than 1 is larger in (a) likelihood ratio order and (b) dispersive order when the scale parameters are more dispersed in the sense of majorization. 相似文献
18.
19.
We obtain precise large deviations for heavy-tailed random sums
, of independent random variables.
are nonnegative integer-valued random variables independent of r.v. (X
i
)i
N with distribution functions F
i. We assume that the average of right tails of distribution functions F
i is equivalent to some distribution function with regularly varying tail. An example with the Pareto law as the limit function is given. 相似文献
20.
研究了在概率空间(Ω,T,P)上,独立的无界随机变量和尾部概率不等式,提出了一种用切割原始概率空间(Ω,T,P)的新型方法去处理独立的无界随机变量和。给出了独立的无界随机变量和的指数型概率不等式。作为结果的应用,一些有趣的例子被给出。这些例子表明:文中提出的方法和结果对研究独立的无界随机变量和的大样本性质是十分有用的。 相似文献