Generalized cumulative residual entropy and record values

The Shannon entropy of a random variable has become a very useful tool in Probability Theory. In this paper we extend the concept of cumulative residual entropy introduced by Rao et al. (in IEEE Trans Inf Theory 50:1220–1228, 2004). The new concept called generalized cumulative residual entropy (GCRE) is related with the record values of a sequence of i.i.d. random variables and with the relevation transform. We also consider a dynamic GCRE obtained using the residual lifetime. For these concepts we obtain some characterization results, stochastic ordering and aging classes properties and some relationships with other entropy concepts.     

Research on emergency dissemination models for social media based on information entropy

ABSTRACT

The emergency information dissemination model discussed in this paper describes the dissemination and broadcasting characteristics of emergency information on the internet. This model is helpful for predicting the occurrence of incidents and improving the emergency response. We construct an emergency information dissemination model based on the information entropy method. We verify the validity of the model by obtaining emergency data from Sina Blog regarding the Ya’an and Wenchuan earthquakes. We find that the level of information entropy significantly influences emergency information dissemination. From the perspective of information entropy, we can more effectively describe and understand information on the internet concerning emergency responses.     

A residual inaccuracy measure based on the relevation transform

Inaccuracy and information measures based on the cumulative residual entropy are useful in various fields, and are attracting increasing attention in Probability Theory and Statistics. In this paper, we introduce and study an inaccuracy measure concerning the relevation transform of two nonnegative continuous random variables. We investigate various distributional properties and characterization results that are based on the mean residual lifetime and involve the generalized Pareto distribution. A connection with the proportional hazards model is also provided. We obtain comparison results involving the proposed inaccuracy measure and some existing inaccuracy measures. Some illustrative examples are finally given.     

Some Properties of Past Entropy and their Applications

In the context of information theory, measure of uncertainty in past lifetime distribution has been proposed by Di Crescenzo and Longobardi (J Appl Probab 39:434–440, 2002). In this paper, we study some ordering and aging properties in terms of past entropy (based on past lifetime) and develop some characterization results. Some discrete distribution results are also addressed here.     

Repeated measures and longitudinal data analysis using higher‐order entropies

This paper implements the generalized maximum entropy (GME) method in longitudinal data setup to investigate the regression para meters and correlation among the repeated measurements. We derive the GME system using Shannon classical entropy as well as some higher‐order entropies assuming an autoregressive correlation structure. This method is illustrated using two simulated examples to study the effect of changing the support range and compare the performance of the GME approach with the classical estimation methods.     

基于时效熵的牛鞭效应研究与仿真分析

在前人研究的基础上,探讨时间因素在牛鞭效应中的影响。将经典熵模型和时间因素结合起来,创造性地构造了基于牛鞭效应的"时效熵"模型。对模型进行了仿真验证,发现熵模型对应的数据与牛鞭效应的大小具有秩一致性。根据熵模型的标示进行仿真发现:随着订货提前期跨度的拉长,牛鞭效应加剧。     

INFORMATION THEORETIC APPROACHES IN ECONOMICS

Economics has seen a recent rise in interest in information theory as an alternative framework to the conventional notion of equilibrium as a fixed state, such as Walrasian market‐clearing general equilibrium. The information theoretic approach is predicated on the notion of statistical equilibrium (SE) that takes a distribution over all possible states as an equilibrium, and therefore predicts the endogenous fluctuations of the system along with its central tendency simultaneously. For this reason, SE approaches can explain the observed data without relying on arbitrary assumptions about random noise and provide useful insights for many interesting economic problems that conventional methods have not been able to satisfactorily deal with. In this paper, we review the key elements of information theory focusing on the notions and applications of entropy and SE in economics, particularly paying attention to how entropy concepts open up a new frontline of economic research.     

Some notes on discount factor restrictions for dynamic optimization problems

We consider dynamic optimization problems on one-dimensional state spaces. Under standard smoothness and convexity assumptions, the optimal solutions are characterized by an optimal policy function h mapping the state space into itself. There exists an extensive literature on the relation between the size of the discount factor of the dynamic optimization problem on the one hand and the properties of the dynamical system x_t+1=h(x_t) on the other hand. The purpose of this paper is to survey some of the most important contributions of this literature and to modify or improve them in various directions. We deal in particular with the topological entropy of the dynamical system, with its Lyapunov exponents, and with its periodic orbits.     

基于声波信号小波包奇异谱熵和支持向量机的断路器故障诊断研究

在断路器投切时伴随着较强的声波信号,它包含了大量断路器状态信息,通过分析声波信号能够特征提取方法,能够为后续故障诊断提供依据。断路器声波信号易受环境因素影响,且包含非线性、非平稳成份,文中利用小波包奇异谱熵的信号特征提取方法对其进行处理,同时使用支持向量机进行故障识别判断。     

A Paradigm for Masking (Camouflaging) Information

This is an expository paper. Here we propose a decision-theoretic framework for addressing aspects of the confidentiality of information problems in publicly released data. Our basic premise is that the problem needs to be conceptualized by looking at the actions of three agents: a data collector, a legitimate data user, and an intruder. Here we aim to prescribe the actions of the first agent who desires to provide useful information to the second agent, but must protect against possible misuse by the third. The first agent is under the constraint that the released data has to be public to all; this in some societies may not be the case.
A novel aspect of our paper is that all utilities—fundamental to decision making—are in terms of Shannon's information entropy. Thus what gets released is a distribution whose entropy maximizes the expected utility of the first agent. This means that the distribution that gets released will be different from that which generates the collected data. The discrepancy between the two distributions can be assessed via the Kullback–Leibler cross-entropy function. Our proposed strategy therefore boils down to the notion that it is the information content of the data, not the actual data, that gets masked. Current practice of "statistical disclosure limitation" masks the observed data via transformations or cell suppression. These transformations are guided by balancing what are known as "disclosure risks" and "data utility". The entropy indexed utility functions we propose are isomorphic to the above two entities. Thus our approach provides a formal link to that which is currently practiced in statistical disclosure limitation.     

Entropy concentration and the empirical coding game

We give a characterization of maximum entropy/minimum relative entropy inference by providing two 'strong entropy concentration' theorems. These theorems unify and generalize Jaynes'concentration phenomenon' and Van Campenhout and Cover's 'conditional limit theorem'. The theorems characterize exactly in what sense a prior distribution Q conditioned on a given constraint and the distribution      minimizing D(P  ‖  Q ) over all P satisfying the constraint are 'close' to each other. We then apply our theorems to establish the relationship between entropy concentration and a game-theoretic characterization of maximum entropy inference of Topsøe and others.     

基于熵定律的产品造型设计原理探析

现代产品是科技与美的凝结,产品造型是传递功能、传达理念、美学诉求的载体。熵定律是普遍存在于自然界、人类社会、精神领域等一切时空的普遍规律,本文从熵定律的角度,并结合格式塔心理学,对产品造型感性需求的深层心理机制、产品复杂度与审美共鸣、低熵整体观的传达等问题作出了剖析,从中总结出指导设计的一些方法原则。     

Maximum entropy autoregressive conditional heteroskedasticity model

In many applications, it has been found that the autoregressive conditional heteroskedasticity (ARCH) model under the conditional normal or Student’s t distributions are not general enough to account for the excess kurtosis in the data. Moreover, asymmetry in the financial data is rarely modeled in a systematic way. In this paper, we suggest a general density function based on the maximum entropy (ME) approach that takes account of asymmetry, excess kurtosis and also of high peakedness. The ME principle is based on the efficient use of available information, and as is well known, many of the standard family of distributions can be derived from the ME approach. We demonstrate how we can extract information functional from the data in the form of moment functions. We also propose a test procedure for selecting appropriate moment functions. Our procedure is illustrated with an application to the NYSE stock returns. The empirical results reveal that the ME approach with a fewer moment functions leads to a model that captures the stylized facts quite effectively.     

Modeling time-varying higher-order conditional moments: A survey

Since the introduction of the Autoregressive Conditional Heteroscedasticity (ARCH) model, the literature on modeling the time-varying second-order conditional moment has become increasingly popular in the last four decades. Its popularity is partly due to its success in capturing volatility in financial time series, which is useful for modeling and predicting risk for financial assets. A natural extension of this is to model time variation in higher-order conditional moments, such as the third and fourth moments, which are related to skewness and kurtosis (tail risk). This leads to an emerging literature on time-varying higher-order conditional moments in the last two decades. This paper outlines recent developments in modeling time-varying higher-order conditional moments in the economics and finance literature. Using the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) framework as a foundation, this paper provides an overview of the two most common approaches for modeling time-varying higher-order conditional moments: autoregressive conditional density (ARCD) and autoregressive conditional moment (ARCM). The discussion covers both the theoretical and empirical aspects of the literature. This includes the identification of the associated skewness–kurtosis domain by using the solutions to the classical moment problems, the structural and statistical properties of the models used to model the higher-order conditional moments and the computational challenges in estimating these models. We also advocate the use of a maximum entropy density (MED) as an alternative method, which circumvents some of the issues prevalent in these common approaches.     

供应链系统道德风险的熵度量研究

道德风险问题直接影响着供应链系统的稳定性和可靠性。本文首先介绍了引起供应链道德风险的因素，建立了基于节点企业与影响因素的风险度矩阵，并对其进行了熵权调整；在此基础上又建立了道德风险的熵度量模型，并对其进行了熵变分析；最后，本文结合外部环境因素的分析，提出了整个供应链系统道德风险的熵度量方法。     

Asymptotic and Bootstrap techniques for testing the expected value of a fuzzy random variable

In this paper we will consider hypothesis-tests for the (fuzzy-valued) mean value of a fuzzy random variable in a population. For this purpose, we will make use of a generalized metric for fuzzy numbers, and we will develop an approach for normal fuzzy random variables, and two different approaches for the case of fuzzy random variables taking on a finite number of different values. A real-life example illustrates the use of the last two approaches. Finally, a comparison between the introduced techniques is developed by means of simulation studies leading to close inferential conclusions.Acknowledgements.The research in this paper has been partially supported by MCYT Grants BFM2002-01057 and BFM2001-3494. Their financial support is gratefully acknowledged. The authors are sincerely grateful to their colleague Gil González-Rodríguez for all his comments and suggestions in connection with this paper; his scientific support has been very valuable. The authors want also thank the referees of the first version of the paper because of their useful hints to improve it.     

Method towards discovering potential opportunity information during cross-organisational business processes using role identification analysis within complex social network

ABSTRACT

The key to discover potential opportunity information in cross-organisation business processes (COBPs) is to identify the primary roles and actors, i.e. how to obtain their associations according to the interactive behaviours within the complex social networks. The information of roles in COBPs is commonly considered important and explicitly related with activities contained in COBPs. In this paper, we define a role as a configurable resource model integrating the capabilities and knowledge required to the qualified actors. Furthermore, we introduce two networks named as role-based interactive behaviour network and handover of work social network to investigate the information on roles. How to build the complex social network mapped on roles from COBPs is also discussed, and an approach to obtain the potential opportunity information is proposed by combining with the significance of roles and actors. The simulation result shows that the primary roles may not completely correspond to the central position in networks, but they are closely associated with more reliable actors.     

Information spillover across international real estate investment trusts: Evidence from an entropy-based network analysis

In this study, we unveil information spillover between international real estate markets using an entropy-based network approach for real estate investment trusts (REIT). Our novel approach is simple and yet flexible enough to accommodate the nature and extent of information spillover among several components of the global housing network. For a network of nine leading industrial economies, we unveil static and time-varying information spillover of REIT returns using total transfer entropy, pairwise net transfer entropy and directional (“From”, “To”) transfer entropy. Evidence suggests that the greatest pairwise transfer entropy is from the US to Australia, whereas France, the Netherlands, New Zealand and Singapore are the largest information recipients in the network. The time-varying evolution of total transfer entropy also exhibits a declining trend for the integration of global housing market during our sample period.     

熵变:企业并购的动因分析

本文简要地评述了国内外学者对企业并购的理论与应用文献。在前辈们的基础上,文章从企业的管理性质——耗散结构入手,解析了企业并购的动因是追求企业的熵变为负。在熵变为负的情况下,企业向社会输入负熵,社会支持企业回报负熵,两者在组成一个开放系统的基础下,达到双赢。     

熵原理在标准化中的应用研究

熵是物理学中的重要概念,熵理论对整个科学来说是第一法则,将熵理解为混乱程度的量度,为熵原理在其他领域的应用打开了缺口。文章回顾了熵原理的发展,分析了熵原理与标准化的关系,并运用熵原理解析了企业标准化系统的运行规律及企业标准运作的终极目标。