Complete Convergenceand Complete Moment Convergence for Weighted Sums of ANA Random Variables

In this paper,we investigate the complete convergence and complete moment conver-gence for weighted sums of arrays of rowwise asymptotically negatively associated(ANA)random variables,without assuming identical distribution.The obtained results not only extend those of An and Yuan[1]and Shen et al.[2]to the case of ANA random variables,but also partially improve them.

On the Strong Laws for Weighted Sums of m-negatively Asso ciated Random Variables

In this article, the author establishes the strong laws for linear statistics that are weighted sums of a m-negatively associated(m-NA) random sample. The obtained results extend and improve the result of Qiu and Yang in [1] to m-NA random variables.

SOME LIMIT THEOREMS FOR WEIGHTED SUMS OF ARRAYS OF NOD RANDOM VARIABLES

In this paper the authors study the complete, weak and almost sure convergence for weighted sums of NOD random variables and obtain some new limit theorems for weighted sums of NOD random variables, which extend the corresponding theorems of Stout [1], Thrum [2] and Hu et al. [3].

Strong Laws of Large Numbers for Weighted Sums of Ч-mixing Sequence

In this paper, strong laws of large numbers for weighted sums of ■-mixing sequence are investigated. Our results extend the corresponding results for negatively associated sequence to the case of ■-mixing sequence.

Supply Chain Finance Credit Risk Evaluation Method Based on Self-Adaption Weight

Credit risk is the core issue of supply chain finance. In the supply chain, problems happened in different enterprises can influent the whole to different degrees through transferring, thus statuses of all enterprises and their different influences should be considered when evaluating the supply chain’s credit risk. We examine the characters of supply chain network and complex network, use the local growing complex network to simulate the real supply chain, use cluster analysis to classify the company into several levels;Introducing each level’s self-adaption weight formula according to the company’s quantity and degrees of this level and use the weight to improve the credit evaluation method. The research results indicate that complex network can be used to simulate the supply chain. The credit risk evaluation (CRE) of an enterprise level with bigger note degrees has a greater weight in the supply chain system’s CRE, thus has greater effect on the whole chain. Considering different influences of different enterprise levels can improve credit risk evaluation method’s sensitivity.

On complete convergence for Stout's type weighted sums of NOD sequence

In this paper, the complete convergence for the weighted sums of independent and identically distributed random variables in Stout [9] is improved and extended under NOD setup.The more optimal moment condition is given. The main results also hold for END sequence.

Almost Sure Convergence and Complete Convergence for the Weighted Sums of Martingale Differences

Let {(D n, FFFn),n/->1} be a sequence of martingale differences and {a ni, 1≤i≤n,n≥1} be an array of real constants. Almost sure convergence for the row sums ?i = 1n ani D1\sum\limits_{i = 1}^n {a_{ni} D_1 } are discussed. We also discuss complete convergence for the moving average processes underB-valued martingale differences assumption.

Equivalent Conditions of Complete Convergence for Weighted Sums of Sequences of Extended Negatively Dependent Random Variables

By using Rosenthal type moment inequality for extended negatively de- pendent random variables, we establish the equivalent conditions of complete convergence for weighted sums of sequences of extended negatively dependent random variables under more general conditions. These results complement and improve the corresponding results obtained by Li et al. （Li D L, RAO M B, Jiang T F, Wang X C. Complete convergence and almost sure convergence of weighted sums of random variables. J. Theoret. Probab., 1995, 8： 49-76） and Liang （Liang H Y. Complete convergence for weighted sums of negatively associated random variables. Statist. Probab. Lett., 2000, 48： 317-325）.

W eighted sum based method on the optimal weights for weapon evaluation

In order to solve instability problem of calculation precision resulting from the selection of each target weight in evaluating weapon systems, a weighted sum based method is proposed. Specif- ically, the subjective weights depending on experts＇ experience are substituted by the optimal weights. The optimal weights are acquired through constructing a mathematical programming model based on subjective weights and objective weights. The method of solving subjective weights is the same as before, and the objective weights were solved by means of grey theory. The case analysis shows that the method of improved weighted sum can improve the evaluation precision up to more than 5% , and minimize the instability of calculation precision resulting from only using subjective weights. The method that the optimal weights substituted the subjective weights is brought forward in improving evaluation precision for the first time. The ideas of the optimal weights and the pro- posed method are described and analyzed.

Almost Sure Convergence of Weighted Sums of NA Sequences

For double arrays of constants {a ni, 1≤i≤k n, n≥1} and NA r.v. 's {X n, n≥1}, conditions for almost sure convergence of are given. Both casesk n ↑ ∞ andk n=∞ are treated. A Marcinkiewicz-type theorem for i. d. NA sequences is obtained as a special case.

Complete Convergence of Weighted Sums for Asymptotically Almost Negatively Associated Sequences

For weighted sums of asymptotically almost negatively associated (AANA) random variables sequences, we use the Rosenthal type moment inequalities and prove the Marcinkiewicz-Zygmund type complete convergence and obtain the complete convergence rates. Our results extend some known ones.

On the Limiting Behavior of Weighted Partial Sums for B Valued Martingale Difference Sequences

Let {Xn, n≥1} be a martingale difference sequence and {a nk , 1?k?n,n?1} an array of constant real numbers. The limiting behavior of weighted partial sums ∑ k=1 n a nk X k is investigated and some new results are obtained.

ON ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF RANDOM ELEMENT SEQUENCES

We mainly study the almost sure limiting behavior of weighted sums of the form ∑ni=1 aiXi/bn , where {Xn, n ≥ 1} is an arbitrary Banach space valued random element sequence or Banach space valued martingale difference sequence and {an, n ≥ 1} and {bn,n ≥ 1} are two sequences of positive constants. Some new strong laws of large numbers for such weighted sums are proved under mild conditions.

Complete Convergence of Weighted Sums for Arrays of Rowwise m-negatively Associated Random Variables

In this paper, we discuss the complete convergence of weighted sums for arrays of rowwise m-negatively associated random variables. By applying moment inequality and truncation methods, the sufficient conditions of complete convergence of weighted sums for arrays of rowwise m-negatively associated random variables are established. These results generalize and complement some known conclusions.

A Precise Asymptotic Behaviour of the Large Deviation Probabilities for Weighted Sums

Let {Xn, n ≥ 1} be a sequence of independent and identically distributed positive valued random variables with a common distribution function F. When F belongs to the domain of partial attraction of a semi stable law with index α, 0 < α < 1, an asymptotic behavior of the large deviation probabilities with respect to properly normalized weighted sums have been studied and in support of this we obtained Chover’s form of law of iterated logarithm.

An Almost Sure Central Limit Theorem for Weighted Sums of Mixing Sequences

In this paper, we prove an almost sure central limit theorem for weighted sums of mixing sequences of random variables without stationary assumptions. We no longer restrict to logarithmic averages, but allow rather arbitrary weight sequences. This extends the earlier work on mixing random variables

Complete Convergence for Weighted Sums of WOD Random Variables

In this article, we study the complete convergence for weighted sums of widely orthant dependent random variables. By using the exponential probability inequality, we establish a complete convergence result for weighted sums of widely orthant dependent random variables under mild conditions of weights and moments. The result obtained in the paper generalizes the corresponding ones for independent random variables and negatively dependent random variables.

Complete Convergence for Weighted Sums of φ-mixing Sequence

In this paper, the complete convergence and strong law of large numbers for weighted sums of φ-mixing sequence with different distribution are investigated under some weaker moment conditions. Our results extend ones of independent sequence with identical distribution to the case of φ-mixing sequence with different distribution.

Several Classes of Two-weight or Three-weight Linear Codes and Their Applications

Recently,linear codes with a few weights have been extensively studied due to their applications in secret sharing schemes,constant composition codes,strongly regular graphs and so on.In this paper,based on the Weil sums,several classes of two-weight or three-weight linear codes are presented by choosing a proper defining set,and their weight enumerators and complete weight enumerators are determined.Furthermore,these codes are proven to be minimal.By puncturing these linear codes,two classes of two-weight projective codes are obtained,and the parameters of the corresponding strongly regular graph are given.This paper generalizes the results of[7].

计及终端模式差异的微电网可靠性评估方法

针对微电网终端模式多元化对其可靠性评估带来的问题,提出了计及终端模式参与度的加权秩和比综合评估方法?首先,从主维度和交互维度建立可靠性评估指标体系,并提出“负荷风光比”和“负荷储能容量比”两个新指标。然后,引入博弈论将网络分析法(analytic network process,ANP)与熵权法(entropy weight method,EWM)结合,得出各指标的组合最优权重。为更好体现出不同终端对微电网可靠性的影响,根据指标类型引入不同终端模式下各指标参与度函数。最后,基于微电网终端模式和指标类型的差异,提出基于终端模式参与度的加权秩和比法(participation-weighted rank-sum ratio,PWRSR)计算综合评价值。以某市的实际数据进行仿真验证。结果表明,所提方法可以充分考虑在不同终端模式下微电网内部的交叉影响,得到更全面、准确的评估结果?