A wealth distribution model with a non-Maxwellian collision kernel

A non-Maxwellian collision kernel is employed to study the evolution of wealth distribution in a multi-agent society.The collision kernel divides agents into two different groups under certain conditions. Applying the kinetic theory of rarefied gases, we construct a two-group kinetic model for the evolution of wealth distribution. Under the continuous trading limit, the Fokker–Planck equation is derived and its steady-state solution is obtained. For the non-Maxwellian collision kernel, we find a suitable redistribution operator to match the taxation. Our results illustrate that taxation and redistribution have the property to change the Pareto index.

Empirical Bayes Test for Two-parameter Exponential Distribution under Type-Ⅱ Censored Samples

The empirical Bayes test problem is considered for scale parameter of twoparameter exponential distribution under type-II censored data.By using wavelets estimation method,the EB test function is constructed,of which the asymptotic optimality and convergence rates are obtained.Finally,an example concerning the main result is given.

BAYESIAN PREDICTION FOR THE TWO-PARAMETER EXPONENTIAL DISTRIBUTION BASED ON TYPE Ⅱ DOUBLY CENSORING

The two-parameter exponential distribution is proposed to be an underlying model,and prediction bounds for future observations are obtained by using Bayesian approach.Prediction intervals are derived for unobserved lifetimes in one-sample prediction and two-sample prediction based on type Ⅱ doubly censored samples.A numerical example is given to illustrate the procedures,prediction intervals are investigated via Monte Carlo method,and the accuracy of prediction intervals is presented.

面向供应链分销的多维空间Pareto边界自动谈判模型研究

随着电子商务的快速发展,自动谈判逐渐成为提升供应链系统效率的一种手段。为了优化多方参与的供应链分销谈判应用,本文将多边多属性谈判问题转化为多目标优化模型,采用改进的非支配遗传算法NSGA-Ⅲ计算多维空间的Pareto边界;然后,设计多线程谈判模型,将参与多方谈判的买卖各方拆解为多个双边谈判线程,分别在多维Pareto边界上进行谈判;进而,采用动态时间依赖策略(DTD),使Agent根据对方报价在Pareto边界上动态调整让步策略,快速达成协议。为验证模型的有效性,本文进行了大量模拟自动谈判实验。实验结果表明,所提出的改进算法和谈判流程优于领域最新研究成果,能有效提升多边多属性谈判效率,有助于多方达成共赢局面。

双边定时截尾下Pareto分布的参数的极大似然估计的EM算法

给出了当寿命分布为Pareto分布时,双边定时截尾寿命试验下形状参数的极大似然估计。由于似然方程形式较复杂,无法得到参数的显式表达式。但可证明此极大似然估计是唯一存在的,并利用EM算法求出了此参数的一种估计。

由Chvátal定理引出的关于Weibull分布和Pareto分布的研究

受Chvátal定理的启发,本文研究了随机变量不超过其期望的概率的下确界问题.利用分析的方法,我们得到了当随机变量的分布为Weibull分布或Pareto分布时该随机变量不超过其期望的概率的下确界.

Generalized Extreme Value-Pareto Distribution Function and Its Applications in Ocean Engineering

In this paper, we establish a generalized extreme Value-Pareto distribution model and derive an analytical expression of Weibull–Pareto distribution model. Based on a data sample of 26-year wave height, we adopt the new model to estimate the design wave height for 500, 700 and 1000-year return periods. Results show that the design wave height from Weibull–Pareto distribution is between that of the Weibull distribution and that of the Pearson-Ⅲ distribution.For the 500-year return period design wave height, the results from the new model is 1.601% lower than those from the Weibull distribution and 1.319% higher than those from the Pearson-Ⅲ distribution. The Weibull–Pareto distribution innovatively considers the fractal features, extreme-value statistics and the truncated data in the derivation process. Therefore, it is a more holistic and practical model for estimating the design parameters in marine and coastal environments.

GENERALIZED PARETO DISTRIBUTION FIT TO MEDICAL INSURANCE CLAIMS DATA

How to choose an optimal threshold is a key problem in the generalized Pareto distribution （GPD） model. This paper attains the exact threshold by testing for GPD,and shows that GPD model allows the actuary to easily estimate high quantiles and the probable maximum loss from the medical insurance claims data.

Estimation of Poisson-Generalized Pareto Compound Extreme Value Distribution by Probability-Weighted Moments and Empirical Analysis

This paper puts forward a Poisson-generalized Pareto (Poisson-GP) distribution. This new form of compound extreme value distribution expands the existing application of compound extreme value distribution, and can be applied to predicting financial risk, large insurance settlement and high-grade earthquake, etc. Compared with the maximum likelihood estimation (MLE) and compound moment estimation (CME), probability-weighted moment estimation (PWME) is used to estimate the parameters of the distribution function. The specific formulas are presented. Through Monte Carlo simulation with sample sizes 10, 20, 50, 100, 1 000, it is concluded that PWME is an efficient method and it behaves steadily. The mean square errors (MSE) of estimators by PWME are much smaller than those of estimators by CME, and there is no significant difference between PWME and MLE. Finally, an example of foreign exchange rate is given. For Dollar/Pound exchange rates from 1990-01-02 to 2006-12-29, this paper formulates the distribution function of the largest loss among the investment losses exceeding a certain threshold by Poisson-GP compound extreme value distribution, and obtains predictive values at different confidence levels.

Generalized Pareto Distribution Model and Its Application to Hydrocarbon Resource Structure Prediction of the Huanghua Depression

The generalized Pareto distribution model is a kind of hydrocarbon pool size probability statistical method for resource assessment. By introducing the time variable, resource conversion rate and the geological variable, resource density, such model can describe not only different types of basins, but also any exploration samples at different phases of exploration, up to the parent population. It is a dynamic distribution model with profound geological significance and wide applicability. Its basic principle and the process of resource assessment are described in this paper. The petroleum accumulation system is an appropriate assessment unit for such method. The hydrocarbon resource structure of the Huanghua Depression in Bohai Bay Basin was predicted by using this model. The prediction results accord with the knowledge of exploration in the Huanghua Depression, and point out the remaining resources potential and structure of different petroleum accumulation systems, which are of great significance for guiding future exploration in the Huanghua Depression.

Transmuted Exponentiated Moment Pareto Distribution

In this work, the authors proposed a four parameter potentiated lifetime model named as Transmuted Exponentiated Moment Pareto (TEMP) distribution and discussed numerous characteristic measures of proposed model. Parameters are estimated by the method of maximum likelihood and performance of these estimates is also assessed by simulations study. Four suitable lifetime datasets are modeled by the TEMP distribution and the results support that the proposed model provides much better results as compared to its sub-models.

极值服从广义Pareto分布的扭转载荷外推方法研究

提出了一种极值样本服从广义Pareto分布(generalized pareto distribution,GPD)函数的扭转载荷时域外推方法,基于极值样本的均值超出函数,首先确定一个区间范围,并以形状参数最小的均方误差为目标,通过自抽样法确定最佳阈值,再采用极大似然估计法对GPD函数的形状参数和尺度参数进行估计,获取扭转随机载荷谱的极值样本,服从GPD分布规律。以商用车驾驶室的稳定杆为研究对象,介绍了扭转载荷采集的方法,基于所提出的扭转载荷时域外推方法进行外推研究,并分别从穿级计数、功率谱密度、雨流图和潜在伪损伤量等方面对外推前后的载荷谱进行了对比分析。结果表明:所构建的载荷外推算法对商用车驾驶室稳定杆扭转载荷外推有较好适应性。

逐步增加Ⅱ型截尾下Pareto分布形状参数的Bayes估计

基于逐步增加Ⅱ型截尾样本,首先得出Pareto分布形状参数的极大似然估计,考虑两个损失函数和形状参数的两个先验分布,得出该分布形状参数的4个Bayes估计。由数值模拟结果发现,上述四个Bayes估计值的均方误差均小于极大似然估计值,其中,当损失函数为二次损失函数,形状参数的先验分布为共轭先验分布时的Bayes估计的均方误差较小,估计效果更理想,且实例分析与数值模拟结果相符。其次在二次损失函数下,针对形状参数先验分布选取共轭先验分布,给出Pareto分布形状参数的多层Bayes估计和E-Bayes估计。

Control charts for the Pareto distribution

The Pareto distribution plays an important role in various areas of research. In this paper, the average run length （ARL） unbiased control charts, which monitor the shape and threshold parameters of the Pareto distribution respectively, are proposed when the incontrol parameters are known. The effects of parameter estimation on the performance of the proposed control charts are also studied. Results show that the control charts with the estimated parameters are not suitable to be used in the known parameter case, thus the ARL-unbiased control charts for the shape and threshold parameters with the desired ARLo, which consider the variability of the parameter estimates, are further developed. The performance of the proposed control charts is investigated in terms of the ARL. Finally, an example is given to illustrate the proposed control charts.

Maximum Likelihood Estimation for Generalized Pareto Distribution under Progressive Censoring with Binomial Removals

The paper deals with the estimation problem for the generalized Pareto distribution based on progressive type-II censoring with random removals. The number of components removed at each failure time is assumed to follow a binomial distribution. Maximum likelihood estimators and the asymptotic variance-covariance matrix of the estimates are obtained. Finally, a numerical example is given to illustrate the obtained

Inference on Constant-Partially Accelerated Life Tests for Mixture of Pareto Distributions under Progressive Type-II Censoring

The main purpose of this paper is to obtain the inference of parameters of heterogeneous population represented by finite mixture of two Pareto (MTP) distributions of the second kind. The constant-partially accelerated life tests are applied based on progressively type-II censored samples. The maximum likelihood estimates (MLEs) for the considered parameters are obtained by solving the likelihood equations of the model parameters numerically. The Bayes estimators are obtained by using Markov chain Monte Carlo algorithm under the balanced squared error loss function. Based on Monte Carlo simulation, Bayes estimators are compared with their corresponding maximum likelihood estimators. The two-sample prediction technique is considered to derive Bayesian prediction bounds for future order statistics based on progressively type-II censored informative samples obtained from constant-partially accelerated life testing models. The informative and future samples are assumed to be obtained from the same population. The coverage probabilities and the average interval lengths of the confidence intervals are computed via a Monte Carlo simulation to investigate the procedure of the prediction intervals. Analysis of a simulated data set has also been presented for illustrative purposes. Finally, comparisons are made between Bayesian and maximum likelihood estimators via a Monte Carlo simulation study.

Application of Pareto Distribution in Wage Models

This paper deals with the use of Pareto distribution in models of wage distribution. Pareto distribution cannot generally be used as a model of the whole wage distribution, but only as a model for the distribution of higher or of the highest wages. It is usually about wages higher than the median. The parameter b is called the Pareto coefficient and it is often used as a characteristic of differentiation of fifty percent of the highest wages. Pareto distribution is so much the more applicable model of a specific wage distribution, the more specific differentiation of fifty percent of the highest wages will resemble to differentiation that is expected by Pareto distribution. Pareto distribution assumes a differentiation of wages, in which the following ratios are the same： ratio of the upper quartile to the median; ratio of the eighth decile to the sixth decile; ratio of the ninth decile to the eighth decile. This finding may serve as one of the empirical criterions for assessing, whether Pareto distribution is a suitable or less suitable model of a particular wage distribution. If we find only small differences between the ratios of these quantiles in a specific wage distribution, Pareto distribution is a good model of a specific wage distribution. Approximation of a specific wage distribution by Pareto distribution will be less suitable or even unsuitable when more expressive differences of mentioned ratios. If we choose Pareto distribution as a model of a specific wage distribution, we must reckon with the fact that the model is always only an approximation. It will describe only approximately the actual wage distribution and the relationships in the model will only partially reflect the relationships in a specific wage distribution.

Characterization of Pareto Distribution Through Expectation of Function of Order Statistics

For characterization of Pareto distribution one needs any arbitrary non constant function only by approach of identity of distribution and equality of expectation of function of random variable in place of approaches such as relation （linear） in （economic variation） reported and true income, independency of suitable function of order statistics, mean and the extreme observation of the sample etc. Examples are given for illustrative purpose

无失效数据场合下Pareto分布可靠度的Bayes估计

在无失效数据场合下,根据Pareto分布的分布函数的上凸函数性质,讨论Pareto分布可靠度的Bayes估计.首先取关于失效概率P_(i)的减函数(1-P_(i))^(a)作为P_(i)先验分布的核函数,给出了可靠度Ri的先验分布,然后计算其Bayes估计,最后进行了算例分析.算例分析结果表明,与取均匀分布作为失效概率的先验分布相比,本文提出的方法有效提高了Pareto分布可靠度的估计精度.