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1.
Let X
1
, X
2 denote positive heavy-tailed random variables with continuous marginal distribution functions F
1 and F
2, respectively. The asymptotic behavior of the tail of X
1
+X
2 is studied in a general copula framework and some bounds and extremal properties are provided. For more specific assumptions on F
1
, F
2 and the underlying dependence structure of X
1 and X
2, we survey explicit asymptotic results available in the literature and add several new cases.Supported by the Austrian Science Fund Project P-18392. 相似文献
2.
Enkelejd Hashorva Anthony G. Pakes 《Journal of Mathematical Analysis and Applications》2010,372(2):496-514
Let X,Y,B be three independent random variables such that X has the same distribution function as YB. Assume that B is a beta random variable with positive parameters α,β and Y has distribution function H with H(0)=0. In this paper we derive a recursive formula for calculation of H, if the distribution function Hα,β of X is known. Furthermore, we investigate the relation between the tail asymptotic behaviour of X and Y, which is closely related to asymptotics of Weyl fractional-order integral operators. We present three applications of our asymptotic results concerning the extremes of two random samples with underlying distribution functions H and Hα,β, respectively, and the conditional limiting distribution of bivariate elliptical distributions. 相似文献
3.
得到一类Gumbel分布最大吸引场的随机容量样本的次序统计量的精致渐近性,揭示了收敛速度、权函数、边界函数及极限状态之间的联系.这类吸引场真包含了全体(γ),γ>0分布族. 相似文献
4.
Zhong Gen Su 《数学学报(英文版)》2008,24(6):971-982
The author considers the largest eigenvaiues of random matrices from Gaussian unitary ensemble and Laguerre unitary ensemble, and the rightmost charge in certain random growth models. We obtain some precise asymptotics results, which are in a sense similar to the precise asymptotics for sums of independent random variables in the context of the law of large numbers and complete convergence. Our proofs depend heavily upon the upper and lower tail estimates for random matrices and random growth models. The Tracy-Widom distribution plays a central role as well. 相似文献
5.
Peggy Tang Strait 《Journal of multivariate analysis》1974,4(4):494-496
It is shown that if X1, X2, …, Xn are symmetric random variables and max(X1, …, Xn)+ = max(0, X1, …, Xn), then E[max(X1,…,Xn)+]=[max(X1,X1,+X2,+X1,+X3,…X1,+Xn)+], and in the case of independent identically distributed symmetric random variables, E[max(X1, X2)+] = E[(X1)+] + (1/2)E[(X1 + X2)+], so that for independent standard normal random variables, E[max(X1, X2)+] = (1/√2π)[1 + (1/√2)]. 相似文献
6.
8.
J. Behboodian 《Journal of Theoretical Probability》1989,2(2):267-270
The symmetry of the sum and product of two independent random variablesX andY, whenX orY is not symmetric, is studied. 相似文献
9.
We study the distribution of the maximum M of a random walk whose increments have a distribution with negative mean which belongs for some γ > 0 to a subclass of the class S γ (for example, see Chover, Ney, and Wainger [5]). For this subclass we provide a probabilistic derivation of the asymptotic tail distribution of M and show that the extreme values of M are in general attained through some single large increment in the random walk near the beginning of its trajectory. We also give some results concerning the “spatially local” asymptotics of the distribution of M, the maximum of the stopped random walk for various stopping times, and various bounds. 相似文献
10.
Gregory Beylkin Lucas Monzón Ignas Satkauskas 《Applied and Computational Harmonic Analysis》2019,46(2):400-416
We introduce a new functional representation of probability density functions (PDFs) of non-negative random variables via a product of a monomial factor and linear combinations of decaying exponentials with complex exponents. This approximate representation of PDFs is obtained for any finite, user-selected accuracy. Using a fast algorithm involving Hankel matrices, we develop a general numerical method for computing the PDF of the sums, products, or quotients of any number of non-negative independent random variables yielding the result in the same type of functional representation. We present several examples to demonstrate the accuracy of the approach. 相似文献
11.
Enkelejd Hashorva Oleg Seleznjev Zhongquan Tan 《Journal of Mathematical Analysis and Applications》2018,457(1):841-867
This contribution is concerned with Gumbel limiting results for supremum with centered Gaussian random fields with continuous trajectories. We show first the convergence of a related point process to a Poisson point process thereby extending previous results obtained in [8] for Gaussian processes. Furthermore, we derive Gumbel limit results for as and show a second-order approximation for for any . 相似文献
12.
Let (X,Y) be a bivariate elliptical random vector with associated random radius in the Gumbel max-domain of attraction. In this paper we obtain a second order asymptotic expansion of the joint survival probability and the conditional probability , for x,y large. 相似文献
13.
14.
Precise asymptotics in the Baum-Katz and davis law of large numbers for positively associated sequences 总被引:5,自引:1,他引:5
§ 1 Introduction and resultsL et { X,Xi;i≥ 1} be a sequence of i.i.d.random variables,and set Sn= ni=1 Xi,n≥1.Hsu and Robbins[1 ] introduced the conceptof complete convergence.They together withErdos[2 ] proved n≥ 1 P(|Sn|≥εn) <∞ ,ε>0 (1)if and only if EX=0 and EX2 <∞ .L ater,Spitzer[3] proved n≥ 11n P(|Sn|≥εn) <∞ ,ε>0if and only if EX =0 and E|X|<∞ .More generally,it was shown by Baum and Katz[4 ]that,for 0
0 (… 相似文献
15.
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
16.
17.
Jiang Chaowei Yang Xiaorong 《高校应用数学学报(英文版)》2007,22(1):87-94
In the case of Zd (d ≥ 2)-the positive d-dimensional lattice points with partial ordering ≤, {Xk,k ∈ Zd } i.i.d. random variables with mean 0, Sn = ∑k≤nXk and Vn2 = ∑j≤nX2j, the precise asymptotics for ∑n1/|n|(log|n|)dP(|Sn/vn|≥ ε√loglog|n|) and ∑n(logn|)δ/|n|(log|n|)d-1 P(|Sn/Vn| ≥ ε√log n), as ε ↘ 0, is established. 相似文献
18.
19.
On the linear combination of normal and Laplace random variables 总被引:2,自引:2,他引:0
Saralees Nadarajah 《Computational Statistics》2006,21(1):63-71
Summary The exact distribution of the linear combination αX+βY is derived when X and Y are normal and Laplace random variables distributed independently of each other. A program in MAPLE is provided to compute
the associated percentage points. 相似文献
20.
In this paper, we obtain sufficient and necessary conditions for local asymptotics for the maximum of a Markov modulated random
walk with long-tailed increments and negative drifts, where the local asymptotics means asymptotic behaviour of P(· ∈ (x, x + z]) for each z > 0, as x→∞. Our results extend and improve the existing ones in the literature. 相似文献