基于凸函数的风险测度

利用凸函数构造了一种新的风险测度,发现它是包含了损失概率、损失期望值、绝对离差、绝对半离差,下偏矩、(α,t)模型、ES等常见方法的更为广泛的风险测度.对其性质的研究发现该风险测度满足凸性和协调性,考虑到凸性以及协调性在投资组合以及风险管理中的重要意义,因此对该风险测度的研究就具有一定的实践和学术价值.     

Spatial risk measures and applications to max-stable processes

The risk of extreme environmental events is of great importance for both the authorities and the insurance industry. This paper concerns risk measures in a spatial setting, in order to introduce the spatial features of damages stemming from environmental events into the measure of the risk. We develop a new concept of spatial risk measure, based on the spatially aggregated loss over the region of interest, and propose an adapted set of axioms for these spatial risk measures. These axioms quantify the sensitivity of the risk measure with respect to the space and are especially linked to spatial diversification. The proposed model for the cost underlying our definition of spatial risk measure involves applying a damage function to the environmental variable considered. We build and theoretically study concrete examples of spatial risk measures based on the indicator function of max-stable processes exceeding a given threshold. Some interpretations in terms of insurance are provided.     

A cost-based importance measure for system components: An extension of the Birnbaum importance

In reliability engineering, component importance measures are used to prioritise components in a system for purposes such as reliability improvement and maintenance planning. Existing importance measures have paid little attention to the costs incurred by maintaining a system and its components within a given time period. Cost-effectiveness analysis, however, is critically important in increasingly competitive markets. This paper proposes a new cost-based importance measure which considers costs incurred by maintaining a system and its components within a finite time horizon. Possible extensions are discussed and examples are given to show the use of the new measure.     

Md2 is not Secure Without the Checksum Byte

In 1989, Ron Rivest introduced the MD2 Message Digest Algorithm which takes as input a message of arbitrary length and produces as output a 128-bit message digest, by appending some redundancy to the message and then iteratively applying a 32 bytes to 16 bytes compression function. MD2 Message Digest Algorithm is one of the most frequently used hashing function with MD4, MD5, SHA, SHA-1. Some attacks against MD4 and MD5 have been presented by Dobbertin. Up to now, no attack against MD2 has been presented.This function has been updated in 1993 in the RFC 1423 document. It was conjectured that the number of operations needed to get two messages having the same message digest is on the order of 2⁶⁴ (using the birthday paradox), and that the complexity of inverting the hash function is on the order of 2¹²⁸ operations. No attack against this function has been published so far. In this paper, we propose a low complexity method to find collisions for the compression function of MD2. The easiness to find these collisions could imply that the first conjecture is false if these collisions can be used to make global collisions for MD2.     

基于系统可靠性的组件综合重要度变化机理分析

重要度理论是一种重要的系统薄弱环节识别和评估方法,被广泛应用于系统可靠性设计优化、维修资源分配、维修决策以及风险分析等领域。本文以组件状态转移率为纽带,分析了组件综合重要度对系统可靠性的影响机理,识别对系统可靠性变化影响最大的组件,综合重要度评估了单位时间内系统可靠性的变化。首先给出综合重要度的定义;其次讨论系统可靠性的组件重要度表示方法;最后在串联和并联系统中,分析综合重要度随着组件状态转移率的变化机理。     

Non-parametric estimation of the generalized past entropy function with censored dependent data

The generalized past entropy function introduced by Gupta and Nanda (2002) is viewed as a dynamic measure of uncertainty in past life. This measure finds applications in modeling past life time data. In the present work we provide non-parametric kernel-type estimator for the generalized past entropy function based on censored data. Asymptotic properties of the estimator are established under suitable regularity conditions. Simulation studies are carried out using the Monte Carlo method.     

基于组合赋权法和未确知测度模型的发动机健康状况评估

为了有效评估航空发动机的健康状况,提出一种逼近理想点的组合赋权法和未确知测度模型相结合的评估方法。首先,分别利用序关系分析法、指标相关性赋权法和指标难度赋权法得到各指标的主客观单一权重;利用逼近理想点的组合赋权法并考虑指标权重与重要性的一致性,求解指标组合权重,使赋权结果更具科学性,加大不同类别评价对象的区分度。其次,基于未确知测度模型,利用K-means算法将各指标分为两个对立等级,每个等级又分为两个互补小等级,以减少信息的重叠进一步区分不同类别的评价对象;根据指标属于不同等级的未确知测度、指标组合权重和评分准则,得到评价对象的健康评分。最后,通过航空发动机实例分析以及与其他方法的对比分析,验证此方法的有效性。     

Singularity of certain self-affine measures

The self-affine measure associated with an iterated function system and a weight is uniquely determined. The problem of determining whether a self-affine measure is absolutely continuous or singular has been studied extensively in recent years. In the present paper we consider the singularity of certain self-affine measures. We obtain a sufficient condition for such measures being singular. Two applications of this result are given, which extend several known results in a simple manner.     

一种面向可靠性的改进不确定性重要度分析方法

作为识别和评估系统薄弱环节的有效工具之一的重要度理论,一直都被广泛应用于系统可靠性和安全性工程。而作为其主要环节的不确定性重要度分析更是扮演着不可或缺的角色。因此,为有效表征多态系统的可靠性,本文给出了一种变换数据处理方式的改进不确定性重要度分析方法。该模型是以两个累积分布函数之间的空间几何距离为基础,通过改变随机输入变量的不确定性范围和对应分布情况,模拟和描述输入对系统输出变量的相对影响趋势,并以两个累积分布函数之间的定积分面积表示。最后利用系统故障树对其进行不确定性重要度分析。结果表明,空间几何距离是一种用来表示输入变化对输出分布变化的相对影响的不确定性重要度度量的有效工具。     

基于交叉熵和Shapley值的犹豫模糊多属性决策方法

针对属性值以犹豫模糊集形式给出的多属性决策问题,将Shapley理论和模糊测度进行结合,提出了两种更加能全面融合信息的诱导型广义犹豫模糊混合Shapley平均(I-GHFHSA)算子和诱导型广义犹豫模糊混合Shapley几何(I-GHFHSG)算子,同时详细研究了它们的相关特性。这两种算子综合考虑了数据不同组合的重要性、数据间的关联性,以及数据位置之间的相互依赖性。考虑到有时会存在属性权重以及数据位置权重未知的多属性决策问题,将交叉熵理论和Shapley函数进行结合,建立了最优模糊测度确定模型。最后提出了一种基于I-GHFHSA算子和I-GHFHSG算子的犹豫模糊多属性决策方法,并通过实际案例验证了其可行性和合理性。     

Note on packing and weak-packing measures with Hausdorff functions

For every Hausdorff function we construct a compact metric space of finite positive weak-packing measure. Also we prove that for every non-doubling Hausdorff function there exists a compact metric space on which the packing and weak-packing measures are not equivalent.     

On some measures of noncompactness in the space of continuous functions

We consider some quantities in the space of functions continuous on a bounded interval, which are related to monotonicity of functions. Based on those quantities we construct a few measures of noncompactness in the mentioned function space. Several properties of those measures are established; among others it is shown that they are regular or “partly” regular measures and equivalent to the Hausdorff measure of noncompactness.     

带权的Sharp函数和极大函数

本文研究带权ｕ的Ｓｈａｒｐ函数和极大函数Ｍ＿ｕｆ之间的关系，首先建立它们（关于测度ωｄｘ）的非增重排函数和之间的一个不等式，进而证明，只要ωｄｘ，ｕｄｘ是可比较测度，当时，就有，其中常数Ｃ与ｆ，ｐ（１≤ｐ＜＋∞）无关。     

A new model for classifying inputs and outputs and evaluating the performance of DMUs based on translog output distance function

In conventional data envelopment analysis it is assumed that the input versus output status of each chosen performance measures is known. In some conditions finding a statue of some variables from the point view of input or output is very difficult; these variables treat as both an input and output and are called flexible measures. This paper proposes a new model based on translog output distance function for classifying inputs and outputs and evaluating the performance of decision-making units by considering flexible measures. Monte Carlo simulation is applied to evaluate the presented model comparing with that of the recent model found in the literature. The result shows that the measure efficiencies of our model are statistically closer to true efficiencies and have higher rank correlation with true efficiencies. Also results obtained from simulated data show that there are high correlation between our model and that of the recent model.     

等价度量下的直径型填充测度

本文研究了在等价度量下,直径型填充测度之间的关系,证明了对任意紧度量空间(X,ρ),Pρ,g和Pcρ,g等价当且仅当纲函数g满足加倍条件.所得结论揭示了填充测度与加倍条件之间的关系.     

凸域的外平行集的包含测度

本文研究了凸域内定长线段的包含测度问题,利用广义支持函数和限弦函数,得到了一类特殊凸域的包含测度.     

A scale elasticity measure for directional distance function and its dual: Theory and DEA estimation

In this paper we focus on scale elasticity measure based on directional distance function for multi-output–multi-input technologies, explore its fundamental properties and show its equivalence with the input oriented and output oriented scale elasticity measures. We also establish duality relationship between the scale elasticity measure based on the directional distance function with scale elasticity measure based on the profit function. Finally, we discuss the estimation issues of the scale elasticity based on the directional distance function via the DEA estimator.     

On the Geometric Densities of Random Closed Sets

Abstract

In many applications it is of great importance to handle evolution equations about random closed sets of different (even though integer) Hausdorff dimensions, including local information about initial conditions and growth parameters. Following a standard approach in geometric measure theory such sets may be described in terms of suitable measures. For a random closed set of lower dimension with respect to the environment space, the relevant measures induced by its realizations are singular with respect to the Lebesgue measure, and so their usual Radon–Nikodym derivatives are zero almost everywhere. In this paper we suggest to cope with these difficulties by introducing random generalized densities (distributions) á la Dirac–Schwarz, for both the deterministic case and the stochastic case. In this last one we analyze mean generalized densities, and relate them to densities of the expected values of the relevant measures. Many models of interest in material science and in biomedicine are based on time dependent random closed sets, as the ones describing the evolution of (possibly space and time inhomogeneous) growth processes; in such a situation, the Delta formalism provides a natural framework for deriving evolution equations for mean densities at all (integer) Hausdorff dimensions, in terms of the local relevant kinetic parameters of birth and growth. In this context connections with the concepts of hazard function, and spherical contact distribution function are offered.     

Distinction between several subsets of fuzzy measures

In this paper, we place several fuzzy measure subsets in relation one with the other. The subsets under study are those corresponding to the definitions of probability measure. Sugeno's g_λ-measure, Shafer's belief function and Zadeh's possibility measure. We study the intersection of these subsets and we show the particular role of Dirac's measures in this comparison. We limit ourself to the case of mappins whose domain is the collection of all subsets of a finite set.Finally, the obtained partial results are summarized in only one figure which shoul clarify the specificity of each of the above definitions.     

P-可测空间及其可测函数

经典集合理论认为集合就是具有一定属性的对象所构成的整体,当一个普通集合的属性发生改变时,由此生成的新的集合称为P-集合.在测度空间上研究P-集合时所生成的新的空间称为P-测度空间.由于任何测度空间均可转化为概率空间,首先利用随机数的产生研究了随机P-集合的产生.然后借助P-可测空间提出了内P-可测映射、内P-可测函数和外P-可测映射、外P-可测函数及P-可测,给出了其有关性质.