Record values from generalized Pareto distribution and associated inference

In this paper, we derive exact explicit expressions for the single, double, triple and quadruple moments of the upper record values from a generalized Pareto distribution. We then use these expressions to compute the mean, variance, and the coefficients of skewness and kurtosis of certain linear functions of record values. Finally, we develop approximate confidence intervals for the location and scale parameters of the generalized Pareto distribution using the Edgeworth approximation and compare them with the intervals constructed through Monte Carlo simulations. Received: June 1999     

The Estimation of Pareto Distribution by a Weighted Least Square Method

The two-parameter Pareto distribution provides reasonably good fit to the distributions of income and property value, and explains many empirical phenomena. For the censored data, the two parameters are regularly estimated by the maximum likelihood estimator, which is complicated in computation process. This investigation proposes a weighted least square estimator to estimate the parameters. Such a method is comparatively concise and easy to perceive, and could be applied to either complete or truncated data. Simulation studies are conducted in this investigation to show the feasibility of the proposed method. This report will demonstrate that the weighted least square estimator gives better performance than unweighted least square estimators with simulation cases. We also illustrate that the weighted least square estimator is very close to maximum likelihood estimator with simulation studies.     

Pareto Density Distributions

Building on new insights into the genesis ofPareto-Distributions,(“Kopp” effect etc.) as publishedearlier in “Quality and Quantity”, the author gives at least oneauthentic/definitive Pareto-Formula. A practical example of the synthetic generation of Pareto Distributions by means of spreadsheets. A working D.I.Y-method for fine-fitting Pareto-curvesto scattergrams with spreadsheets using interalia an indirect method of the least squares of residuals is fully demonstrated. A comparative test-fit to a cumulative Pareto- Distribution example, where a simulative curve-formula evolved by Prof. B. Arnold/Ucla is used for demonstration. Easy to absorb and to retain graphical tableaux are employed to visualize the chain of descent and interconnections between normal distributions, log-normal distributions and Pareto- Distributions. A quasi-dichotomy of the Pareto-formulae is presented in tableau-form. One innovative formula for Pareto-distribution is given as: F(x)= k^*e― [((ln(Integral(In(x)))) ‐ (ln(Integral(ln(μ)))))² / 2^*(ln(Integral(ln(σ))))²} Readers e-mailed constructive opinions &/or inputs are encouraged and welcomed. This revised version was published online in June 2006 with corrections to the Cover Date.     

帕累托法则在仓库盘点中的应用

帕累托法则是数理统计中的一种重要方法,文中通过对仓库盘点进行分析,介绍了如何根据帕累托法则进行仓库盘点及补充措施。     

On the structure of Pareto optimal cake partitions

We study Pareto optimal partitions of a “cake” among n players. Each player uses a countably additive non-atomic probability measure to evaluate the size of pieces of cake. We present two geometric pictures appropriate for this study and consider the connection between these pictures and the maximization of convex combinations of measures, which we studied in Barbanel and Zwicker [Barbanel, J.B., Zwicker, W., 1997. Two applications of a theorem of Dvoretsky, Wald, and Wolfovitz to cake division. Theory and Decision 43, 203–207].     

A Note on the Prediction Intervals for a Future Ordered Observation from a Pareto Distribution

In the researching of products' reliability, the result of life testing is used as the basis for the evaluation and improvement of reliability. During life testing, however, the future observation in an ordered sample is often expected to be predicted so as to show how long a sample of units might run until all fail in life testing. Therefore, we propose five new pivotal quantities to obtain prediction intervals of future order statistics based on right type II censored samples from the Pareto distribution with known shape parameter, then compares the lengths of the prediction intervals when using the pivotal quantity of Ouyang and Wu (1994) based on best linear unbiased estimator (BLUE) of scale parameter, and these five pivotal quantities. An advantage of these five pivotal quantities is that these are easier to calculate than the pivotal quantity of Ouyang and Wu (1994) based on BLUE of scale parameter, since they need to compute the tables of coefficients of BLUE of scale parameter.     

A social procedurial approach to the Pareto optimization problematique

This article applies a variant of game theory to the Pareto multi-value problematique, that is situations where members of a group, community or society are faced with alternative allocations, institutional arrangements, or states of the world and may collectively choose an allocation, institutional arrangement or state of the world if they can agree on it. This type of multiple value decision situation is increasingly prevalent not only on the level of societal and political issues but on the level of many enterprises, particularly those advocating corporate social responsibility. Because actors hold and apply values from different perspectives, there are potential contradictory value judgments and incompatible equilibria. In a world of contradiction, incommensurability, and disequilibrium, to what extent can conflicts be resolved and social equilibrium accomplished? Force works but it is inherently unstable. Drawing on an extension of classical game theory, generalized game theory (GGT), this article addresses the multi-value problematique in terms of collective “resolution procedures.” These regulative procedures—or social algorithms—are applied to problems of conflict and suboptimality in a multiple value world such as Pareto envisioned. This paper (the first of two) outlines key elements of GGT, defines the Pareto multi-value problematique, pointing out several of the critical weaknesses, theoretical as well as empirical, of the Pareto approach. GGT is then applied in defining and analyzing several major procedures to realize improvements in a multi-value world characterized by conflict and sub-optimality. A second article conceptualizes a complex of societal games making up a social system with 2-phase multi-level game processes; it applies the conceptualization to the different societal procedures for multi-value choice under conditions of conflict. Procedures such as democratic voting, adjudication and administrative decision-making, and multi-lateral negotiation are capable of producing outcomes that in many cases are widely accepted as legitimate and become social equilibria (at least within some range of conditions). These procedures and the conditions for their activation and implementation are modelled and explicated through a generalized game approach.     

人力资源管理中的帕累托定律

人力资源管理是组织管理中的重要内容,文章提出运用帕累托定律进行核心人力资源的管理以带动整个组织的成员,力求以最小投入得到最大产出。     

Partition ratios, Pareto optimal cake division, and related notions

We consider the problem of partitioning a ‘cake' C among n players. Various criteria have been considered for deciding whether a partition P₁,P₂,…,P_n of C, where piece P_i goes to player i, is a ‘good' partition. See, for example, Barbanel (1996) [Barbanel, J.B., 1996. Super envy-free cake division and independence of measures. J. Math. Anal. Appl. 197, 54–60] or Brams and Taylor (1996) [Brams, S.J., Taylor, A.D., 1996. Fair Division: From Cake-Cutting To Dispute Resolution. Cambridge Univ. Press]. In this paper we study certain real numbers (the ‘partition ratios' of this paper's Section 2) which can be associated in a natural way with any partition. We show that various types of products of these numbers provide us with useful information about certain trades and transfers between players.     

Improved estimation of extreme quantiles in the multivariate Lomax (Pareto II) distribution

Estimation of a quantile of the common marginal distribution in a multivariate Lomax (Pareto II) distribution with unknown location and scale parameters is considered. For quadratic loss and specified extreme quantiles, it is established that the best affine equivariant procedure is inadmissible by constructing a better estimator.     

A conceptual framework for product lifecycle modelling

Product lifecycle modelling is to define and represent product lifecycle data and to maintain data interdependencies. To build a complete, reusable and highly consistent product lifecycle information model, the product lifecycle is divided into five stages: requirement analysis, conceptual design, engineering design, manufacturing, and service and support. Accordingly, five stage product models (requirement analysis model, conceptual design model, engineering design model, manufacturing model, and service and support model) are discussed. To integrate all information of a product lifecycle and support networked manufacturing mode, the key elements of product lifecycle modelling are discussed and a framework of product lifecycle modelling is proposed. Further, the relationship and evolvement of product models at different stages are described. Finally, a Web-based integration framework is proposed to support interoperability of distributed product data sources.     

Pareto optimality in continuous-time OLG economies

The aim of this paper is the achievement of a complete characterization of the Pareto optimality of competitive equilibria for deterministic, pure exchange, continuous-time economies with a countable number of overlapping generations, where each consumer’s life-span consists in a bounded interval of time. For such an environment, we obtain separate sufficient and necessary conditions for Pareto optimality in the form of the Cass’ criterion, that is, in terms of the equilibrium prices. However, these conditions are not equivalent in general. Therefore, in order to get that equivalence we are compelled to impose certain restrictions, either on consumers’ lifetimes, assuming that all of them have the same longevity, or on the dynamic behaviour of relative intertemporal equilibrium prices. In both cases, we are able to derive a single condition that is sufficient and necessary for efficiency, thus achieving full characterizations.     

One-Sample Bayesian Predictive Interval of Future Ordered Observations for the Pareto Distribution

Nigm et al. (2003, statistics 37: 527–536) proposed Bayesian method to obtain predictive interval of future ordered observation Y _(j) (r < j≤ n ) based on the right type II censored samples Y ₍₁₎ < Y ₍₂₎ < ... < Y _(r) from the Pareto distribution. If some of Y ₍₁₎ < ... < Y _(r-1) are missing or false due to artificial negligence of typist or recorder, then Nigm et al.’s method may not be an appropriate choice. Moreover, the conditional probability density function (p.d.f.) of the ordered observation Y _(j) (r < j ≤ n ) given Y ₍₁₎ <Y ₍₂₎ < ... < Y _(r) is equivalent to the conditional p.d.f. of Y _(j) (r < j ≤ n ) given Y _(r). Therefore, we propose another Bayesian method to obtain predictive interval of future ordered observations based on the only ordered observation Y _(r), then compares the length of the predictive intervals when using the method of Nigm et al. (2003, statistics 37: 527–536) and our proposed method. Numerical examples are provided to illustrate these results.     

考虑无转移支付的VMI系统Pareto改进

收益共享机制下的转移支付是影响供应商积极实施VMI的关键因素。在当前处于强势地位的下游企业不愿意提供转移支付的情况下,如何实现VMI系统的Pareto改进呢?将转移支付成本与物流供应商采用业务延伸策略为项目型企业提供终端产品所产生的成本领先优势进行比较发现,业务延伸策略下的VMI既弥补了无转移支付对供应商所造成的经济损失,又帮助项目型企业节省了实施自我服务策略时所投入的相关成本,如库存成本和加工设备成本,从而实现了VMI系统的Pareto改进。     

Joint confidence region for the parameters of pareto distribution

The Pareto distribution is commonly used by economists as a model for the distribution of incomes. Separate confidence intervals or approximate confidence intervals for the parameters of Pareto distribution were discussed by some authors. This paper discusses exact joint confidence region for the parameters of Pareto distribution. The method can be used for both complete samples and type II censored samples.     

次优和非最优的一般分析:方法的创新

本文运用理性预期思想和随机等价方法开拓性地研究了资源配置的效率,包括帕累托最优（无约束帕累托最优和有约束帕累托最优）和非帕累托最优。基本结论是,一个资源配置中所有商品价格波动的总方差等于零等价于在二阶条件具备下其处于帕累托最优状态,也等价于资源配置满足无约束条件下的怕累托最优条件或有约束条件下的帕累托次优条件;而总方差大于零等价于资源配置处于非帕累托最优状态;总方差与资源配置中期望价格的比值越小,则这个配置的效率越高,反之,则越低。最后,设计了一个“信息逐步披露的预期帕累托改进”模型,讨论了非帕累托最优配置的改进途径及其政策含义。     

Sharp exponential and entropy bounds on expectations of generalized order statistics

Sharp lower and upper bounds on expected values of generalized order statistics are proven by the use of Moriguti's inequality combined with the Young inequality. The bounds are expressed in terms of exponential moments or entropy. They are attainable providing new characterizations of some nontrivial distributions. Received October 2001/Revised May 2002     

Linearity of regression for non-adjacent order statistics

Let X ₁,X ₂,…,X _n be a random sample from a continuous distribution with the corresponding order statistics X _1:n≤X _2:n≤…≤X _n:n. All the distributions for which E(X _{k+r: n}|X _k:n)=a X _k:n+b are identified, which solves the problem stated in Ferguson (1967). Received February 1998     

About inheritance distribution

In this work, we propose two axiomatic procedures to distribute an inheritance based on monetary compensations. In a cooperative context, the differences among the agents’ evaluations of the goods are used to increase everyone’s participation. When the goods’ valuations are heterogeneous each agent gets much more than 1/n of the value he believes the inheritance has.The two procedures are characterized by three criteria, namely: money preservation, Pareto optimality, and a certain kind of proportionality. The difference of the procedures is determined by the kind of proportionality used.