A new generalized Weibull distribution in income economic inequality curves

Researchers have been developing various extensions and modified forms of the Weibull distribution to enhance its capability for modeling and fitting different data sets. In this note, we investigate the potential usefulness of the new modification to the standard Weibull distribution called odd Weibull distribution in income economic inequality studies. Some mathematical and statistical properties of this model are proposed. We obtain explicit expressions for the first incomplete moment, quantile function, Lorenz and Zenga curves and related inequality indices. In addition to the well-known stochastic order based on Lorenz curve, the stochastic order based on Zenga curve is considered. Since the new generalized Weibull distribution seems to be suitable to model wealth, financial, actuarial and especially income distributions, these findings are fundamental in the understanding of how parameter values are related to inequality. Also, the estimation of parameters by maximum likelihood and moment methods is discussed. Finally, this distribution has been fitted to United States and Austrian income data sets and has been found to fit remarkably well in compare with the other widely used income models.     

基尼系数合意值和警戒线的探讨

 近年来，很多学者对基尼系数的经验法则尤其是警戒线提出了质疑。本文首先分析了收入分配的合意类型，然后依据相对贫困、贫富差距及中等收入者的收入份额三个指标来界定合意的收入分配，最后根据合意收入分配确定基尼系数的合意值和警戒线。本文结论表明，0.3—0.4可以被认为是基尼系数的合意值,0.4作为基尼系数警戒线也是比较合理的。     

Gini’s nuclear family

The purpose of this paper is to justify the use of the Gini coefficient and two close relatives for summarizing the basic information of inequality in distributions of income. To this end we employ a specific transformation of the Lorenz curve, the scaled conditional mean curve, rather than the Lorenz curve as the basic formal representation of inequality in distributions of income. The scaled conditional mean curve is shown to possess several attractive properties as an alternative interpretation of the information content of the Lorenz curve and furthermore proves to yield essential information on polarization in the population. The paper also provides asymptotic distribution results for the empirical scaled conditional mean curve and the related family of empirical measures of inequality.      

A fast splitting procedure for classification trees

This paper provides a faster method to find the best split at each node when using the CART methodology. The predictability index is proposed as a splitting rule for growing the same classification tree as CART does when using the Gini index of heterogeneity as an impurity measure. A theorem is introduced to show a new property of the index : the for a given predictor has a value not lower than the for any split generated by the predictor. This property is used to make a substantial saving in the time required to generate a classification tree. Three simulation studies are presented in order to show the computational gain in terms of both the number of splits analysed at each node and the CPU time. The proposed splitting algorithm can prove computational efficiency in real data sets as shown in an example.     

Societal Inequality and individual subjective well-being: Results from 68 societies and over 200,000 individuals, 1981–2008

Income inequality has been contentious for millennia, a source of political conflict for centuries, and is now widely feared as a pernicious “side effect” of economic progress. But equality is only a means to an end and so must be evaluated by its consequences. The fundamental question is: What effect does a country's level of income inequality have on its citizens' quality of life, their subjective well-being? We show that in developing nations inequality is certainly not harmful but probably beneficial, increasing well-being by about 8 points out of 100. This may well be Kuznets's inverted “U”: In the earliest stages of development some are able to move out of the (poorly paying) subsistence economy into the (better paying) modern economy; their higher pay increases their well-being while simultaneously increasing inequality. In advanced nations, income inequality on average neither helps nor harms. Estimates are from random-intercept fixed-effects multi-level models, confirmed by over four dozen sensitivity tests. Data are from the pooled World Values/European Values Surveys, Waves 1 to 5 with 169 representative national samples in 68 nations, 1981 to 2009, and over 200,000 respondents, replicated and extended in the European Quality of Life Surveys.     

中国快递业发展的区域不平衡性测度研究

选取大陆31个省份2007—2014年样本数据,分别测算三区域、八区域分组下快递业发展的不平衡性及极化趋势。研究结果表明:中国快递业发展存在较强的区域不平衡性,且这种不平衡性还呈现不断加大趋势;东中西快递业发展不平衡性明显,总体呈现东部强中西部弱的特点,基尼系数分解结果显示,东中西组间差异为不平衡性贡献了70%以上的份额,同时东部和西部地区内部也存在相当程度的不平衡性;八区域不平衡性也非常明显,总体呈现沿海强内陆弱、东强西弱、南强北弱的基本格局,组间差异贡献了88%左右的份额,就区域内而言,南部沿海和西北地区不平衡性较强,东部沿海、长江中游及东北地区则较为平衡;三区域及八区域分组下快递业不平衡发展均呈现出不断增强的极化趋势。     

On a control chart for the Gini index with simulations

In this work we suggest the use of the Gini index on control charts. The asymptotic properties of Gini index are presented and the control charts based on appropriate confidence intervals are constructed. The suitability of the proposed charts are investigated by means of extensive simulations.     

我国互联网扩散之地区差异的影响因素探究

基于创新扩散理论,对我国互联网扩散的地区不平衡状况及其影响因素进行了初步探索。研究采用基尼系数概念来描述互联网发展的地区不平衡,并通过回归分析探究影响互联网扩散的关键因素。研究发现,近年来我国的互联网发展的地区差距在不断缩小,其差异程度逐渐和经济发展水平的差异程度接近。而决定中国不同省份之间互联网扩散差异的主要因素是随着时间推移而有所变化的。在扩散的早期阶段,经济因素(人均GDP)具有显著影响;随着扩散过程的继续,其他因素如消费结构和生活方式也对互联网扩散有一定程度的作用。     

影响我国居民收入分配差距因素的实证分析

世界银行2005年发展报告显示,中国的基尼系数按由低到高排名第85位,2007年达到了0.48,超过了国际上0.4的警戒线。本文对中国1994—2007年的相关统计资料进行实证分析,以验证税收、转移支付和教育与收入分配差距之间遵从的演变路径,探讨了城乡转移支付对收入分配差距的影响力度,得出结论:教育和税收能缩小收入分配差距,但影响有限;现行的社会保障制度并没有实现制度上的公平,农村社保制度对收入差距的负面影响远大于城市社保制度。