共查询到20条相似文献,搜索用时 368 毫秒
1.
Consider a discrete-time risk model with insurance and financial risks in a stochastic economic environment. Assume that the insurance and financial risks form a sequence of independent and identically distributed random vectors with a generic random vector following a wide type of dependence structure. An asymptotic formula for the finite-time ruin probability with subexponential insurance risks is derived. In doing so, the subexponentiality of the product of two dependent random variables is investigated simultaneously. 相似文献
2.
Yang Yang Remigijus Leipus Jonas Šiaulys Yuquan Cang 《Journal of Mathematical Analysis and Applications》2011,383(1):215-225
This paper investigates the finite-time ruin probability in the dependent renewal risk model, where the claim sizes are independent and identically distributed random variables with strongly subexponential tails, and the interarrival times are negatively dependent. We establish an asymptotic estimate, which holds uniformly for the time horizon varying in the positive half line. 相似文献
3.
This paper considers a bidimensional renewal risk model with constant interest force and dependent subexponential claims. Under the assumption that the claim size vectors form a sequence of independent and identically distributed random vectors following a common bivariate Farlie–Gumbel–Morgenstern distribution, we derive for the finite-time ruin probability an explicit asymptotic formula. 相似文献
4.
This paper addresses the following classical question: Given a sequence of identically distributed random variables in the domain of attraction of a normal law, does the associated linear process satisfy the central limit theorem? We study the question for several classes of dependent random variables. For independent and identically distributed random variables we show that the central limit theorem for the linear process is equivalent to the fact that the variables are in the domain of attraction of a normal law, answering in this way an open problem in the literature. The study is also motivated by models arising in economic applications where often the innovations have infinite variance, coefficients are not absolutely summable, and the innovations are dependent. 相似文献
5.
Osamu Hiwatashi Masaru Nagisa Hiroaki Yoshida 《Probability Theory and Related Fields》1999,113(1):115-133
In usual probability theory, various characterizations of the Gaussian law have been obtained. For instance, independence
of the sample mean and the sample variance of independently identically distributed random variables characterizes the Gaussian
law and the property of remaining independent under rotations characterizes the Gaussian random variables. In this paper,
we consider the free analogue of such a kind of characterizations replacing independence by freeness. We show that freeness
of the certain pair of the linear form and the quadratic form in freely identically distributed noncommutative random variables,
which covers the case for the sample mean and the sample variance, characterizes the semicircle law. Moreover we give the
alternative proof for Nica's result that the property of remaining free under rotations characterizes a semicircular system.
Our proof is more direct and straightforward one.
Received: 12 February 1997 / Revised version: 16 June 1998 相似文献
6.
I. V. Rodionov 《Moscow University Mathematics Bulletin》2014,69(1):1-4
The consistency and asymptotic normality of the Hill estimator of the extreme value index is considered for a sample from a sequence of independent and identically distributed random variables with asymptotically increasing additive impurity. In addition, the cases when the statistical construction of the estimator is possible are analyzed. 相似文献
7.
8.
Enno Mammen 《Probability Theory and Related Fields》1992,93(4):439-455
Summary We show for an i.i.d. sample that bootstrap estimates consistently the distribution of a linear statistic if and only if the normal approximation with estimated variance works. An asymptotic approach is used where everything may depend onn. The result is extended to the case of independent, but not necessarily identically distributed random variables. Furthermore it is shown that wild bootstrap works under the same conditions as bootstrap.This work has been supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 123 Stochastische Mathematische Modelle 相似文献
9.
Ferenc Móricz 《Archiv der Mathematik》2006,86(4):375-384
In recent years, the almost sure central limit theorem attracted widespread attention in Probability Theory. It involves the
harmonic (also called logarithmic) averages of a certain numerical sequence formed from a sequence of independent, identically
distributed random variables. Our primary aim is to study the convergence behavior of the sequence of harmonic averages of
a given numerical sequence from the viewpoint of Summability Theory.
Received: 12 May 2005; revised: 1 July 2005 相似文献
10.
The object of the present investigation is to show that the elegant asymptotic almost-sure representation of a sample quantile for independent and identically distributed random variables, established by Bahadur [1] holds for a stationary sequence of φ-mixing random variables. Two different orders of the remainder term, under different φ-mixing conditions, are obtained and used for proving two functional central limit theorems for sample quantiles. It is also shown that the law of iterated logarithm holds for quantiles in stationary φ-mixing processes. 相似文献
11.
Sharp upper and lower bounds are obtained for the reliability functions and the expectations of lifetimes of coherent systems based on dependent exchangeable absolutely continuous components with a given marginal distribution function, by use of the concept of Samaniego's signature. We first show that the distribution of any coherent system based on exchangeable components with absolutely continuous joint distribution is a convex combination of distributions of order statistics (equivalent to the k-out-of-n systems) with the weights identical with the values of the Samaniego signature of the system. This extends the Samaniego representation valid for the case of independent and identically distributed components. Combining the representation with optimal bounds on linear combinations of distribution functions of order statistics from dependent identically distributed samples, we derive the corresponding reliability and expectation bounds, dependent on the signature of the system and marginal distribution of dependent components. We also present the sequences of exchangeable absolutely continuous joint distributions of components which attain the bounds in limit. As an application, we obtain the reliability bounds for all the coherent systems with three and four exchangeable components, expressed in terms of the parent marginal reliability function and specify the respective expectation bounds for exchangeable exponential components, comparing them with the lifetime expectations of systems with independent and identically distributed exponential components. 相似文献
12.
Elia Liitiäinen Francesco Corona Amaury Lendasse 《Journal of multivariate analysis》2010,101(4):811-823
In this paper we consider the problem of estimating E[(Y−E[Y∣X])2] based on a finite sample of independent, but not necessarily identically distributed, random variables . We analyze the theoretical properties of a recently developed estimator. It is shown that the estimator has many theoretically interesting properties, while the practical implementation is simple. 相似文献
13.
《Statistics & probability letters》1988,6(6):383-388
A locally asymptotically normal estiamtion problem generated by independent and identically distributed generalized random variables is considered. A recursive estimate based on a stochastic approximation method, a modification of an estimate proposed by Sakrison, is shown to be locally asymptotically minimax. For a nonparametric generalization of the estimation problem, a modification of the estimate is shown locally asymptotically minimax adaptive. 相似文献
14.
华志强 《纯粹数学与应用数学》2015,(4):360-366
从保险的实际出发,研究服从长尾分布族(L族)上的多元风险模型中随机变量序列的部分和的精确大偏差,其中假设随机变量序列是一列延拓负相依(END)的、同分布的随机变量序列,利用基于求L族的精确大偏差的方法得到了随机变量部分和的渐近下界. 相似文献
15.
Jason Fulman 《Annals of Combinatorics》2006,10(3):319-332
Bolthausen used a variation of Stein’s method to give an inductive proof of the Berry-Esseen theorem for sums of independent,
identically distributed random variables. We modify this technique to prove a Berry-Esseen theorem for character ratios of
a random representation of the symmetric group on transpositions. An analogous result is proved for Jack measure on partitions.
Received March 11, 2005 相似文献
16.
Let X and Y be two nonnegative and dependent random variables following a generalized Farlie-Gumbel-Morgenstern distribution. In this short note, we study the impact of a dependence structure of X and Y on the tail behavior of XY. We quantify the impact as the limit, as x→∞, of the quotient of Pr(XY>x) and Pr(X∗Y∗>x), where X∗ and Y∗ are independent random variables identically distributed as X and Y, respectively. We obtain an explicit expression for this limit when X is regularly varying or rapidly varying tailed. 相似文献
17.
该文得到了关于一般可分距离空间上独立随机元序列的几乎处处中心极限定理(almost sure central limit theory, 简记为ASCLT). 作为应用, 该文给出了取值于可分Banach空间上随机元序列以及一类随机场序列满足ASCLT的充分条件,最后给出了关于多维随机变量序列极值的ASCLT. 相似文献
18.
In this paper, we obtain the asymptotics for the tail probability of the total claim amount with negatively dependent claim
sizes in two cases: in the first case, the distribution tail of the claim number is dominatedly varying; in the second case,
the distribution of the claim number is in the maximum domain of attraction of the Gumbel distribution, and the claim sizes
are light-tailed. In both cases, we assume that the claim sizes are nondegenerate negatively dependent and identically distributed
random variables and that the claim number is not necessarily independent of the claim sizes. As applications, we derive asymptotics
for the finite-time ruin probabilities in some dependent compound renewal risk models with constant interest rate. 相似文献
19.
S.S. Nayak 《Stochastic Processes and their Applications》1984,17(1):167-176
In this paper, the almost sure limit points and the moments of the number of boundary crossings of some functions of record times, inter-record times and the frequency of record values of a sequence of independent and identically distributed continuous random variables are studied. 相似文献
20.
Gundelinde Maria Wiegel 《Stochastic Processes and their Applications》2018,128(6):1988-2006
Our subject of interest is a simple symmetric random walk on the integers which faces a random risk to be killed. This risk is described by random potentials, which are defined by a sequence of independent and identically distributed non-negative random variables. To determine the risk of taking a walk in these potentials we consider the decay of the Green function. There are two possible tools to describe this decay: The quenched Lyapunov exponent and the annealed Lyapunov exponent. It turns out that on the integers and on regular trees we can state a precise relation between these two. 相似文献