An Estimator of Shannon Entropy of Beta-Generated Distributions and a Goodness-of-Fit Test

The aim of this article is twofold: on the one hand to introduce and study some of the statistical properties of an estimator for the Shannon entropy and on the other hand to develop a goodness-of-fit test for beta-generated distributions and the distribution of order statistics. Beta-generated distributions are a broad class of univariate distributions which has received great attention during the last 15 years, as it obeys nice properties and it extends the distribution of order statistics. The proposed estimator of Shannon entropy of beta-generated distributions is motivated by the respective Vasicek’s estimator, as the latter one is tailored to the class of the beta-generated distributions and the distribution of order statistics. The estimator of Shannon entropy is defined and its consistency is studied. It is, moreover, exploited to build a goodness-of-fit test for the beta-generated distribution and the distribution of order statistics. Simulations are performed to examine the small- and moderate-sample properties of the proposed estimator and to compare the power of the proposed test with the power of competitors under a variety of alternatives.     

A hierarchy of lorenz curves based on the generalized tukey's lambda distribution

A hierarchy of Lorenz curves based on the generalized Tukey's Lambda distribution is proposed. Representations of the corresponding distribution and density function are also provided, together with popular inequality measures. Estimation methods are suggested. Finally, a comparison with other parametric families of Lorenz curves is established.     

对多目标线性规划的λ－算法的修正

本文指出运用多目标线性规划λ－算法在某些情况下会得出错误的结果，分析了发生错误的原因，并给出修正的λ－算法．     

税收、转移支付与顶层收入不平等

顶层收入不平等影响社会经济的平衡与充分发展。通过构建个人所得税和转移支付影响顶层收入不平等的理论模型,使用微观数据库实证分析中国财政体系(个人所得税和转移支付)对顶层收入不平等的影响。理论分析发现,顶层收入者面临的税率越高、获得的补贴程度越小,顶层收入不平等程度越低;顶层收入者的收入增长速度越快、收入波动幅度越大,顶层收入不平等越严重。实证结果显示:顶层收入者面临的实际税率与顶层收入不平等呈反向相关关系,其获得的补贴程度、收入增长速度和收入标准差与顶层收入不平等呈正向相关关系;中国的财政体系对顶层收入不平等的缓解作用有限,且在考虑隐性收入后顶层收入不平等程度更为严重;发达国家的财政体系在缓解顶层收入不平等方面效果显著,发展中国家的财政体系对顶层收入不平等的缓解作用十分有限。中国应当继续完善个人所得税体系和转移支付体系,规范收入分配秩序,减少隐性收入,借鉴域外国家财政体系构建经验完善中国的财政体系,最终缓解顶层收入不平等。     

Bayesian inference for a common scale parameter of several Pareto populations

This article deals with the problem of Bayesian inference concerning the common scale parameter of several Pareto distributions. Bayesian hypothesis testing of, and Bayesian interval estimation for, the common scale parameter is given. Numerical studies including a comparison study, a simulation study, and a practical application study are given in order to illustrate our procedures and to demonstrate the performance, advantages, and merits of the Bayesian procedures over the classical and generalized variable procedures.     

Characterization of probability distributions through higher order gap

Weibull, Burr, Pareto and power function distributions have been characterized through the conditional moments of order statistics with higher gap and some of its important deductions are discussed.     

需求扰动下生产规模不经济闭环供应链的应急渠道决策

针对生产规模不经济闭环供应链，在突发事件干扰其产品的市场需求发生扰动的情况下，比较研究了各类回收渠道分散式决策系统和集中式决策系统的应急均衡决策及契约协调问题。结果表明：当需求的扰动程度不大时，各类系统正常运营环境下新产品的订购量和废旧品的回收量等均衡决策均具鲁棒性，当需求的扰动程度较大时，各类系统均应按其扰动方向调整正常运营环境下制定的均衡决策；制造商回收渠道分散式决策系统中其获得的利润和系统的总利润均高于零售商回收渠道分散式决策系统的，且制造商会利用更高比例的废旧品生产再造品，因此其应直接回收废旧品；各企业的利润和系统的总利润均随生产规模不经济弹性系数的增加而降低；设计的应急收益费用共享契约可协调解决各类回收渠道分散式决策系统中存在的"双重边际效应"问题，且各企业可通过讨价还价确定收益费用共享比例的取值来获得帕累托改进的利润。     

On detecting outliers in the Pareto distribution

In this paper, we introduce two new statistics for detecting outliers in the Pareto distribution. These new statistics are the extension of the statistics for detecting outliers in exponential and gamma distributions. In fact, we compare the power of our test statistics with the other statistics and select the best test statistic for detecting outliers in the Pareto distribution. Finally, numerical examples of different insurance claims are used to see the performance of the test.     

Pareto analysis for the lifetime performance index of products on the basis of progressively first-failure-censored batches under balanced symmetric and asymmetric loss functions

One of the most important topics in manufacturing industries is the evaluation of performance lifetimes of products. Based on a given lifetime performance index, this paper deals with evaluating the performance of a process subject to a given lower specification limit. We confine ourselves to the progressively first-failure-censored data coming from a common Pareto distribution. With both the Bayesian and the non-Bayesian approaches being investigated here, we pay more attention to Bayesian estimators under balanced type loss functions. The results are presented under the balanced versions of two well-known loss functions, namely the squared error loss and the Varian's linear-exponential (LINEX) loss. Moreover, based on the Bayesian and the non-Bayesian approaches, the problem of testing hypotheses on the lifetime performance index is studied. Also, a simulation study is performed to assess the obtained results. Finally, two illustrative examples are given.     

Decision interactions of the monetary and fiscal authorities in the choice of policy mix

Abstract

This article presents an analysis of the states of equilibrium and Pareto optimality of the solutions in the monetary-fiscal games between the fiscal and monetary authorities each having either two or three qualitatively different strategies: expansive, neutral and restrictive. Two sets of assumptions about the influence, exerted by the instruments of the monetary policy (real interest rate) and by those of the fiscal policy (budgetary deficit related to the GDP), on the state of economy (rate of economic growth and inflation) are considered. The results obtained indicate that, along with the case of the prisoner's dilemma, to which the discussion in the major publications on the subject is limited, other situations may also occur, where the independent decisions of the central bank and the government do not necessarily lead to the choice of a Pareto non-optimal solution.