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Evidence from micro-data shows that capital incomes are exceedingly volatile, which makes up a disproportionately high contribution to the overall inequality in populations with the heavy-tailed nature on the income distributions for many countries. The quintile share ratio (QSR) is a recently introduced measure of income inequality, also forming part of the European Laeken indicators and which cover four important dimensions of social inclusion (health, education, employment and financial poverty). In 2001, the European Council decided that income inequality in the European Union member states should be described using a number of indicators including the QSR. Non-parametric estimation has been developed on the QSR index for heavy-tailed capital incomes distributions. However, this method of estimation does not give satisfactory statistical performances, since it suffers badly from under coverage, and so we cannot rely on the non-parametric estimator. Hence, we need another estimator in the case of heavy-tailed populations. This is the reason why we introduce, in this paper, a class of semi-parametric estimators of the QSR index of economic inequality for heavy-tailed income distributions. Our methodology is based on the extreme value theory, which offers adequate statistical results for such distributions. We establish their asymptotic distribution, and through a simulation study, we illustrate their behavior in terms of the absolute bias and the median squared error. The simulation results clearly show that our estimators work well. [ABSTRACT FROM AUTHOR]

A two-parameter unit distribution and its regression model plus its extension to 0 and 1 inflation is introduced and studied. The distribution is called the unit upper truncated Weibull (UUTW) distribution, while the inflated variant is called the 0−1 inflated unit upper truncated Weibull (ZOIUUTW) distribution. The UUTW distribution has an increasing and a J-shaped hazard rate function. The parameters of the proposed models are estimated by the method of maximum likelihood estimation. For the UUTW distribution, two practical examples involving household expenditure and maximum flood level data are used to show its flexibility and the proposed distribution demonstrates better fit tendencies than some of the competing unit distributions. Application of the proposed regression model demonstrates adequate capability in describing the real data set with better modeling proficiency than the existing competing models. Then, for the ZOIUUTW distribution, the CD34+ data involving cancer patients are analyzed to show the flexibility of the model in characterizing inflation at both endpoints of the unit interval.

The aim of this paper is to classify the post-transition OECD countries according to the Gini coefficient for income inequality, the S80/S20 ratio, the income share of the bottom 40% of the population, educational attainment – tertiary education, and labor force participation rate using factor and cluster analyses. Factor analysis resulted in two extracted factors, and factor scores were calculated. Hierarchical and non-hierarchical cluster analysis was performed on factor scores to classify eight posttransition OECD countries and three candidate countries. The research question of this paper is to investigate whether there are similarities/differences between existing members and candidates for membership in the OECD, among the selected post-transition countries of Europe, in the context of income inequality. Based on the dendrogram obtained by the hierarchical Ward’s method, a three cluster solution was selected. The non-hierarchical k-means method for the three-cluster solution clustered Croatia with Bulgaria and Romania. These three countries are OECD candidate countries. Our findings confirm that the three candidate countries remain behind because of historical reasons and the non-implementation of structural reforms.

Inequality indices are quantitative scores that take values in the unit interval, with a zero score denoting complete equality. They were originally created to measure the heterogeneity of wealth metrics. In this study, we focus on a new inequality index based on the Fourier transform that demonstrates a number of intriguing characteristics and shows great potential for applications. By extension, it is demonstrated that other inequality measures, such as the Gini and Pietra indices, can be usefully stated in terms of the Fourier transform, allowing us to illuminate characteristics in a novel and straightforward manner. [ABSTRACT FROM AUTHOR]

Abstract Background An analysis of the regional distribution of health resources is one of the tools for evaluating equal geographic access to health care. The usual analytical approach to an assessment of regional differences is to evaluate each health resource separately. This is a sensible approach, because there may be systematic reasons for any differences, for example, higher salaries in urban areas. However, a separate evaluation of the regional distribution of health resource capacities may be misleading. We should evaluate all health resource capacities as a whole and consider the substitutability of resources. Objective This study aims to measure regional inequalities in the Czech Republic with the help of alternative approaches to the evaluation of regional inequalities in the case of several substitutable health resources. Methods Five alternative evaluation methods (models) are described and applied: the separate evaluation, expert model, market model, common weights model, and production frontier model. Results The regional distribution of physicians and nurses in the Czech Republic in 2017 was evaluated. In spite of many regulations at the national and regional levels, we have found inequalities in regional resource distribution. The models that consider all health resources and the possibility of a resource substitution show lower inequalities between regional health resource capacities. Conclusion Both researchers and policy-makers should always consider the possibility of resource substitutions in the assessment of regional inequalities.

We propose a new four-parameter lifetime model with flexible hazard rate called the Burr XII Power Cauchy (BXII-PC) distribution. We derive the BXII-PC distribution via (ⅰ) the T-X family technique and (ⅱ) nexus between the exponential and gamma variables. The new proposed distribution is flexible as it has famous sub-models such as Burr XII-half Cauchy, Lomax-power Cauchy, Lomax-half Cauchy, Log-logistic-power Cauchy, log-logistic-half Cauchy. The failure rate function for the BXII-PC distribution is flexible as it can accommodate various shapes such as the modified bathtub, inverted bathtub, increasing, decreasing; increasing-decreasing and decreasing-increasing-decreasing. Its density function can take shapes such as exponential, J, reverse-J, left-skewed, right-skewed and symmetrical. To illustrate the importance of the BXII-PC distribution, we establish various mathematical properties such as random number generator, moments, inequality measures, reliability measures and characterization. Six estimation methods are used to estimate the unknown parameters of the proposed distribution. We perform a simulation study on the basis of the graphical results to demonstrate the performance of the maximum likelihood, maximum product spacings, least squares, weighted least squares, Cramer-von Mises and Anderson-Darling estimators of the parameters of the BXII-PC distribution. We consider an application to a real data set to prove empirically the potentiality of the proposed model.

Top incomes are often related to Pareto distribution. To date, economists have mostly used Pareto Type I distribution to model the upper tail of income and wealth distribution. It is a parametric distribution, with interesting properties, that can be easily linked to economic theory. In this paper, we first show that modeling top incomes with Pareto Type I distribution can lead to biased estimation of inequality, even with millions of observations. Then, we show that the Generalized Pareto distribution and, even more, the Extended Pareto distribution, are much less sensitive to the choice of the threshold. Thus, they can provide more reliable results. We discuss different types of bias that could be encountered in empirical studies and, we provide some guidance for practice. To illustrate, two applications are investigated, on the distribution of income in South Africa in 2012 and on the distribution of wealth in the United States in 2013. [ABSTRACT FROM AUTHOR]

Copyright of Revista de Economia Contemporânea is the property of Revista de Economia Contemporanea and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Inequality indices are quantitative scores that take values in the unit interval, with a zero score denoting complete equality. They were originally created to measure the heterogeneity of wealth metrics. In this study, we focus on a new inequality index based on the Fourier transform that demonstrates a number of intriguing characteristics and shows great potential for applications. By extension, it is demonstrated that other inequality measures, such as the Gini and Pietra indices, can be usefully stated in terms of the Fourier transform, allowing us to illuminate characteristics in a novel and straightforward manner.

In this study, we have discussed various statistical properties for 3-component mixture of Rayleigh distributions. Here initially, the main properties of mixture distributions are presented and analyzed. Second, some of the famous entropies, measures of inequality are also discussed. Also, the statistical properties of the density functions of rth-, 1st- and nth-order statistics are derived. Moreover, the parameters estimation of the considered mixture model under the maximum likelihood (ML) estimation is also performed using censored and complete data scheme. Finally, the results on ML estimation are also computed via Monte Carlo simulation study and as well as by using a real-life data set.

Background: An analysis of the regional distribution of health resources is one of the tools for evaluating equal geographic access to health care. The usual analytical approach to an assessment of regional differences is to evaluate each health resource separately. This is a sensible approach, because there may be systematic reasons for any differences, for example, higher salaries in urban areas. However, a separate evaluation of the regional distribution of health resource capacities may be misleading. We should evaluate all health resource capacities as a whole and consider the substitutability of resources.Objective: This study aims to measure regional inequalities in the Czech Republic with the help of alternative approaches to the evaluation of regional inequalities in the case of several substitutable health resources.Methods: Five alternative evaluation methods (models) are described and applied: the separate evaluation, expert model, market model, common weights model, and production frontier model.Results: The regional distribution of physicians and nurses in the Czech Republic in 2017 was evaluated. In spite of many regulations at the national and regional levels, we have found inequalities in regional resource distribution. The models that consider all health resources and the possibility of a resource substitution show lower inequalities between regional health resource capacities.Conclusion: Both researchers and policy-makers should always consider the possibility of resource substitutions in the assessment of regional inequalities. [ABSTRACT FROM AUTHOR]

The purpose of the article is to present ways to measure inequality. The article describes the last three ways to measure inequality, i.e. based on the Lorenz curve, generalized entropy and the social welfare function. It omits, however, the share and division measures, i.e. the absolute and relative differences, variance, quartile and standard deviations, or positional inequality measures based on percentiles, deciles, quartiles, quantiles, the coefficient of variation and the McLoone index, which results from the fact that although they are often used in empirical research, they illustrate division rather than inequality sensu stricto [i.a. Park 1984, pp. 42-44; Heshmati 2004; Jóźwiak, Podgórski 2012; Jabkowski 2009, pp. 32-35]. Thus, the article does not include a wider presentation of these measures.

This paper will propose an index for measuring spatial concentration, which is based on the solution of a particular transportation problem. This approach extends a new index proposed for the measurement of seasonality to the spatial case, and it takes into account the level of the concentration of the phenomenon of interest according to its spatial distribution. Various properties of the proposed index, which make it a desirable measure for spatial concentration, will also be described. An empirical application, using data from selected European countries, will be provided, and the results derived from the proposed index will be compared with those derived from currently used indices. [ABSTRACT FROM AUTHOR]

The objective of the paper is to verify if income inequality impedes the growth rates in OECD countries in the period of 1990–2014 and to reveal whether the choice of the income inequality measure determines the sign and the strength of the estimated relationship. We use system GMM to estimate parameters of a dynamic panel growth model. The research indicates that income inequality negatively affects economic growth. We also find evidence that various measures of inequality bring the different scale of consequences for economic growth, with measures that give more weight to the middle part of the distribution being the weakest predictor of GDP growth. Simultaneously, we present the test of weak instruments, which helps to explain these differences. [ABSTRACT FROM AUTHOR]

It is argued that the political feasibility of climate mitigation policies depends heavily on their distributional effects. This paper therefore studies the distributional effects of the European Commission's Fit-for-55 package at the household level in seven EU countries, analyzing a carbon tax on transport and heating fuels as well as variations of a lump-sum refund. Based on the resulting income distributions, different inequality measures are computed. The paper aims to extend previous methodological approaches by including inequality measures such as the Theil index and Atkinson index and comparing the results of carbon taxes on transport and heating fuels for seven EU countries in a consistent manner. I find that a household-size specific lump-sum refund not only mitigates the negative distributional effects of a carbon tax but also reduces overall inequality compared to the baseline scenario without a tax. [ABSTRACT FROM AUTHOR]

Variability of a microsite contributes to the size hierarchy in tree populations. Tree size symmetry varies with the available growth resources. However, competition hierarchy may not cause size symmetry in tree populations. The identification of mechanisms that determine size hierarchy has ecological significance in the management of a forest stand. Therefore, this study investigated the tree size structure of the Teak stand in the Hilltop and Valley-Bottom stands of the Omo Forest Reserve. A ten-year-old Teak plantation was delineated into Hilltop and Valley-Bottom stands based on topography. Five (30 m × 30 m) sample plots were systematically demarcated on 1 km transects in each stand. Tree stems with diameter at breast height (dbh) ≥ 10 cm were enumerated. Diameter at breast height and total height were measured using Girth tape and Spiegel Relaskop. Stem size inequality, diversity and stand attributes of both stands were evaluated for diameter and height. Data collected were analyzed using descriptive, correlation, regression analysis and t-test at α0.05. Mean dbh and height in the Valley-Bottom stand (11.30 ± 4.82 cm dbh and 7.26 ± 3.21 m) were not significantly different from the Hilltop stand (10.19 ± 4.62 cm dbh and 7.12 ± 3.88 m). Stem density in the Hilltop stand (1431.0 stems/ha) was higher than in Valley-Bottom stand (1248.0 stems/ha). All distributions expressed unimodality, except the diameter distribution of the Valley-Bottom stand, which expressed bimodality. The inequality was strongly correlated with the diversity indices in dbh and height distributions in the Hilltop and Valley-Bottom stands, respectively. The same mechanism was responsible for the dbh and height structures of the Hilltop and Valley-Bottom stands, respectively. However, different mechanisms were responsible for the dbh and height structures of the Valley-Bottom and Hilltop stands, respectively.

The residential sector has become the second largest energy consumer in China. Urban residential energy consumption (URE) in China is growing rapidly in the process of urbanization. This paper aims to reveal the spatiotemporal dynamic evolution and influencing mechanism of URE in China. The spatiotemporal heterogeneity of URE during 2007–2018 is explored through Kernel density estimation and inequality measures (i.e., Gini coefficient, Theil index, and mean logarithmic deviation). Then, with several advantages over traditional index decomposition analysis approaches, the Generalized Divisia Index Method (GDIM) decomposition is employed to investigate the impacts of eight driving factors on URE. Furthermore, the national and provincial decoupling relationships between URE and residential income increase are studied. It is found that different provinces’ URE present a significant agglomeration effect; the interprovincial inequality in URE increases and then decreases during the study period. The GDIM decomposition results indicate the income effect is the main positive factor driving URE. Besides, urban population, residential area, per capita energy use, and per unit area energy consumption positively influence URE. By contrast, per capita income, energy intensity, and residential density have negative effects on URE. There is evidence that only three decoupling states, i.e., weak decoupling, strong decoupling, and expansive negative decoupling, appear in China during 2007–2018. Specifically, weak decoupling is the dominant state among different regions. Finally, some suggestions are given to speed up the construction of energy-saving cities and promote the decoupling process of residential energy consumption in China. This paper fills some research gaps in urban residential energy research and is important for China’s policymakers.

On one hand, a large class of inequality measures, which includes the generalized entropy, the Atkinson, the Gini, etc., for example, has been introduced in P.D. Mergane, G.S. Lo, Appl. Math. 4 (2013), 986–1000. On the other hand, the influence function (IF) of statistics is an important tool in the asymptotics of a nonparametric statistic. This function has been and is being determined and analyzed in various aspects for a large number of statistics. We proceed to a unifying study of the IF of all the members of the so-called Theil-like family and regroup those IF's in one formula. Comparative studies become easier.

• Quantile random forests are estimated to study stock-return predictability. • Quarterly UK data tracing back to 1977 are studied. • Data feature six different inequality measures. • Strong evidence that inequality measures predict stock returns in sample. • No systematic evidence that inequality measures predict stock returns out-of-sample. We contribute to research on the predictability of stock returns in two ways. First, we use quantile random forests to study the predictive value of various consumption-based and income-based inequality measures across the quantiles of the conditional distribution of stock returns. Second, we examine whether the inequality measures, measured at a quarterly frequency, have out-of-sample predictive value for stock returns at three different forecast horizons. Our results suggest that the inequality measures have predictive value for stock returns in sample, but do not systematically predict stock returns out of sample. [ABSTRACT FROM AUTHOR]

In this paper, we consider an extended version of new generalized Lindley distribution (NGLD). We refer to this new generalization as the extended new generalized Lindley distribution (ENGLD). A comprehensive account of the mathematical properties of the new distribution including estimation is presented. A real life data set is considered here to illustrate the relevance of the new model and compared it with other forms of Lindley models using method of moment estimation and method of maximum likelihood estimation.

This paper analyses the gross inland energy consumption (EC) in the European Union countries (EU-15) over the period 2005-2014. The standard tools in the measurement of income inequality such as Lorenz curves, Gini index, Generalized Entropy indices and Atkinson ones are applied. Our empirical results, obtained through the decomposition of the generalized entropy indices, confirm that there are a small inward shift in the corresponding Lorenz curves, that the inequality distribution of EC across the EU-15 countries has decreased (the Gini coefficient falls from 44,27% in 2005 to 42,16% in 2014) and there are huge differences among the countries’ clusters: Mediterranean, Continental, Nordic and Anglo-Saxon. This paper makes a good contribution to knowledge since it uses a very up-to-dated database (Eurostat) and fills a gap in the literature.

A two-parameter unit distribution and its regression model plus its extension to 0 and 1 inflation is introduced and studied. The distribution is called the unit upper truncated Weibull (UUTW) distribution, while the inflated variant is called the 0 - 1 inflated unit upper truncated Weibull (ZOIUUTW) distribution. The UUTW distribution has an increasing and a J-shaped hazard rate function. The parameters of the proposed models are estimated by the method of maximum likelihood estimation. For the UUTW distribution, two practical examples involving household expenditure and maximum flood level data are used to show its flexibility and the proposed distribution demonstrates better fit tendencies than some of the competing unit distributions. Application of the proposed regression model demonstrates adequate capability in describing the real data set with better modeling proficiency than the existing competing models. Then, for the ZOIUUTW distribution, the CD34+ data involving cancer patients are analyzed to show the flexibility of the model in characterizing inflation at both endpoints of the unit interval., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2023 The Author(s).)

To study reliability problems, life time and survival analysis, a new mixture model, called the 3-component mixture of the Exponential distributions, is introduced. This study is mainly concerned with the problem of investigating the different statistical properties of the newly developed 3-component mixture of Exponential distributions. Firstly, some basic properties of the 3-component mixture model are discussed. Secondly, we discuss hazard rate function, cumulative hazard rate function, reversed hazard rate function, mean residual life function, and mean waiting time function. Different measures of entropy and inequality indices are also discussed. Closed form expressions of the density functions of order statistics and their statistical properties are derived. Finally, the parameters of the proposed mixture distribution are estimated by making use of the maximum likelihood approach under complete and censored sampling. The results on maximum likelihood estimation are also supported through a simulation study and a real-life data. [ABSTRACT FROM AUTHOR]

It is sometimes observed and frequently assumed that top incomes in household surveys worldwide are poorly measured and that this problem biases the measurement of income inequality. This paper tests this assumption and compares the performance of reweighting and replacing methods designed to correct inequality measures for top-income biases generated by data issues such as unit or item non-response. Results for the European Union’s Statistics on Income and Living Conditions survey indicate that survey response probabilities are negatively associated with income and bias the measurement of inequality downward. Correcting for this bias with reweighting, the Gini coefficient for Europe is revised upwards by 3.7 percentage points. Similar results are reached with replacing of top incomes using values from the Pareto distribution when the cut point for the analysis is below the 95th percentile. For higher cut points, results with replacing are inconsistent suggesting that popular parametric distributions do not mimic real data well at the very top of the income distribution.

This paper conducts an examination of log files originating from High Performance Computing (HPC) applications with known reliability problems. The results of this study further the maturation and adoption of meaningful metrics representing HPC system and application failure characteristics. Quantifiable metrics representing the reliability of HPC applications are foundational for building an application resilience methodology critical in the realization of exascale supercomputing. In this examination, statistical inequality methods originating from the study of economics are applied to health and status information contained in HPC application log files. The main result is the derivation of a new failure index metric for HPC—a normalized representation of parallel application volatility and/or resiliency to complement existing reliability metrics such as mean time between failure (MTBF), which aims for a better presentation of HPC application resilience. This paper provides an introduction to a Failure Index (FI) for HPC reliability and takes the reader through a use-case wherein the FI is used to expose various run-time fluctuations in the failure rate of applications running on a collection of HPC platforms. [ABSTRACT FROM AUTHOR]

Copyright of Revista Latinoamericana de Metodología de las Ciencias Sociales is the property of Universidad Nacional de La Plata and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Abstract: In recent years traditional inequality measures have been used to quite a considerable extent to examine the international distribution of environmental indicators. One of the main characteristics of these measures is that each one assigns different weights to the changes that occur in the different sections of the variable distribution and, consequently, the results they yield can potentially be very different. Hence, we suggest the appropriateness of using a range of well-recommended measures to achieve more robust results. We also provide an empirical test for the comparative behaviour of several suitable inequality measures and environmental indicators in the international context. Our findings support the hypothesis that in some cases there are differences among measures in both the sign of the evolution over time and its size. [Copyright &y& Elsevier]

Data published by the United Kingdom's Ministry for Justice clearly shows that, compared to persons who were White, members of racial minorities in England, particularly Blacks, were far more likely to be stopped and searched by the police. The question is whether such racial disparity in stops and searches could be justified by racial disparities in offending? Or whether the disparity in stop and searches exceeded the disparity in offending? This paper proposes a method for measuring the amount of excess in racial disparity in police stop and searches. Using the most recently published Ministry of Justice data (for 2007/08) for Police Areas in England and Wales it concludes that while in several Areas there was no excess to racial disparity in police stop and searches, there was, on the basis of the methodology proposed in the paper, evidence of such excess in some Police Areas of England and Wales. [ABSTRACT FROM AUTHOR]

This paper analyses the effects that income nonresponse has on certain well-known inequality coefficients (e.g. Gini, Theil and Atkinson indexes). A number of statistical methods have been developed to impute missing values of incomes for nonrespondents. By simulating several patterns of income nonresponse on actual sub-samples of the Argentinean household survey, this essay analyses the effects that different correction methods produce on a set of inequality coefficients. It is proved that methods often used to correct for nonresponse can introduce important biases on inequality coefficients if the patterns of missingness assumed by such methods do not coincide with the actual pattern. [ABSTRACT FROM AUTHOR]

The article offers information on a study that analyzed progressivity of value added tax (VAT) in the Czech Republic under the framework of both annual incidence and lifetime incidence. It also examined the impact of the harmonisation of VAT rates connected with the accession of the Czech Republic to the European Union on the income distribution. Based on the results, the authors described Czech VAT as regressive when annual income is analysed. Additionally, a lifetime income analysis illustrated a progressive VAT.

While making location decisions, the distribution of distances (outcomes) among the service recipients (clients) is an important issue. In order to comply with the minimization of distances as well as with an equal consideration of the clients, mean-equity approaches are commonly used. They quantify the problem in a lucid form of two criteria: the mean outcome representing the overall efficiency and a scalar measure of inequality of outcomes to represent the equity (fairness) aspects. The mean-equity model is appealing to decision makers and allows a simple trade-off analysis. On the other hand, for typical dispersion indices used as inequality measures, the mean-equity approach may lead to inferior conclusions with respect to the distances minimization. Some inequality measures, however, can be combined with the mean itself into optimization criteria that remain in harmony with both inequality minimization and minimization of distances. In this paper we introduce general conditions for inequality measures sufficient to provide such an equitable consistency. We verify the conditions for the basic inequality measures thus showing how they can be used in location models not leading to inferior distributions of distances. [ABSTRACT FROM AUTHOR]