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Equality of opportunity is about leveling the playing field so that circumstances such as gender, ethnicity, place of birth, or family background do not influence a person's life chances. Success in life should depend on people's choices, effort and talents, not to their circumstances at birth. 'Measuring Inequality of Opportunities in Latin America and the Caribbean' introduces new methods for measuring inequality of opportunities and makes an assessment of its evolution in Latin America over a decade. An innovative Human Opportunity Index and other parametric and non-parametric techniques are presented for quantifying inequality based on circumstances exogenous to individual efforts. These methods are applied to gauge inequality of opportunities in access to basic services for children, learning achievement for youth, and income and consumption for adults.

Background Higher levels of socioeconomic deprivation have been consistently associated with increased risk of premature mortality, but a detailed analysis by causes of death is lacking in Belgium. We aim to investigate the association between area deprivation and all-cause and cause-specific premature mortality in Belgium over the period 1998–2019. Methods We used the 2001 and 2011 Belgian Indices of Multiple Deprivation to assign statistical sectors, the smallest geographical units in the country, into deprivation deciles. All-cause and cause-specific premature mortality rates, population attributable fraction, and potential years of life lost due to inequality were estimated by period, sex, and deprivation deciles. Results Men and women living in the most deprived areas were 1.96 and 1.78 times more likely to die prematurely compared to those living in the least deprived areas over the period under study (1998–2019). About 28% of all premature deaths could be attributed to socioeconomic inequality and about 30% of potential years of life lost would be averted if the whole population of Belgium faced the premature mortality rates of the least deprived areas. Conclusion Premature mortality rates have declined over time, but inequality has increased due to a faster pace of decrease in the least deprived areas compared to the most deprived areas. As the causes of death related to poor lifestyle choices contribute the most to the inequality gap, more effective, country-level interventions should be put in place to target segments of the population living in the most deprived areas as they are facing disproportionately high risks of dying.

In this paper, we consider some results about the effect of double truncation on income inequality measures. We present some properties and characterization of inequality measures and truncated distributions and introduce some structural relationships between truncated and original variables in the context of reliability and economics measures. Also, some properties of Lorenz order with truncated distributions are studied. Furthermore, it is shown that the Gini index of doubly truncated was computed by original distribution function and vitality function. Finally, an illustrative example is used for clarifying presented concepts.

The Gini coefficient is a measure of statistical dispersion that is commonly used as a measure of inequality of income, wealth or opportunity. Empirical research has shown that the coefficient may have a nonnegligible downward bias when data are grouped. It is unknown under which grouping conditions the downward bias occurs. In this note it is shown that the Gini coefficient strictly decreases if the data are partitioned into equal sized groups.

Entropy has been proposed as a significant tool for an analysis of spatial differences. Using Semple and Gauthier’s (1972) transformation of the Shannon entropy statistic into an entropy measure of inequality and their algorithm, an estimation is made of changes in regional inequality in Poland over the years 2005–2012. The inequality is decomposed into total, inter- and intra-regional types, and an analysis is made of relations holding between them.

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.

The adage “the rich are getting richer” refers to increasingly skewed and heavily-tailed income distributions. For such distributions, the mean is not the best measure of the center, but the classical indices of income inequality, including the celebrated Gini index, are mean based. In view of this, it has been proposed in the literature to incorporate the median into the definition of the Gini index. In the present paper we make a further step in this direction and, to acknowledge the possibility of differing viewpoints, investigate three median-based indices of inequality. These indices overcome past limitations, such as: (1) they do not rely on the mean as the center of, or a reference point for, income distributions, which are skewed, and are getting even more heavily skewed; (2) they are suitable for populations of any degree of tail heaviness, and income distributions are becoming increasingly such; and (3) they are unchanged by, and even discourage, transfers among the rich persons, but they encourage transfers from the rich to the poor, as well as among the poor to alleviate their hardship. We study these indices analytically and numerically using various income distribution models. Real-world applications are showcased using capital incomes from 2001 and 2018 surveys from fifteen European countries.

This paper is concerned with the problem of ranking Lorenz curves in situations where the Lorenz curves intersect and no unambiguous ranking can be attained without introducing weaker ranking criteria than first-degree Lorenz dominance. To deal with such situations, Aaberge (Soc Choice Welf 33:235–259, 2009 ) introduced two alternative sequences of nested dominance criteria for Lorenz curves, which proved to characterize two separate systems of nested subfamilies of inequality measures. This paper uses the obtained characterization results to arrange the members of two different generalized Gini families of inequality measures into subfamilies according to their relationship to Lorenz dominance of various degrees. Since the various criteria of higher degree Lorenz dominance provide convenient computational methods, these results can be used to identify the largest subfamily of the generalized Gini families, and thus the least restrictive social preferences, required to reach unambiguous ranking of a set of Lorenz curves. We further show that the weight-functions of the members of the generalized Gini families offer intuitive interpretations of higher degree Lorenz dominance, which generally has been viewed as difficult to interpret because they involve assumptions about third and higher derivatives. To demonstrate the usefulness of these methods for empirical applications, we examine the time trend in income and earnings inequality of Norwegian males during the period 1967–2005.

Addressing health inequity is a central component of the Sustainable Development Goals and a priority of the World Health Organization (WHO). WHO supports countries in strengthening their health information systems in order to better collect, analyze and report health inequality data. Improving information and research about health inequality is crucial to identify and address the inequalities that lead to poorer health outcomes. Building analytical capacities of individuals, particularly in low-resource areas, empowers them to build a stronger evidence-base, leading to more informed policy and programme decision-making. However, health inequality analysis requires a unique set of skills and knowledge. This paper describes three resources developed by WHO to support the analysis of inequality data by non-statistical users using Microsoft Excel, a widely used and accessible software programme. The resources include a practical eLearning course, which trains learners in the preparation and reporting of disaggregated data using Excel, an Excel workbook that takes users step-by-step through the calculation of 21 summary measures of health inequality, and a workbook that automatically calculates these measures with the user’s disaggregated dataset. The utility of the resources is demonstrated through an empirical example.

Background Monitoring inequalities based on subnational regions is a useful practice to unmask geographical differences in health, and deploy targeted, equity-oriented interventions. Our objective is to describe, compare and contrast current methods of measuring subnational regional inequality. We apply a selection of summary measures to empirical data from four low- or middle-income countries to highlight the characteristics and overall performance of the different measures. Methods We use data from Demographic and Health Surveys conducted in Bangladesh, Egypt, Ghana and Zimbabwe to calculate subnational regional inequality estimates for reproductive, maternal, newborn, and child health services generated from 11 summary measures: pairwise measures included high to low absolute difference, high to low relative difference, and high to low ratio; complex measures included population attributable risk, weighted variance, absolute weighted mean difference from overall mean, index of dissimilarity, Theil index, population attributable risk percentage, coefficient of variation, and relative weighted mean difference from overall mean. Four of these summary measures (high to low absolute difference, high to low ratio, absolute weighted mean difference from overall mean, and relative weighted mean difference from overall mean) were selected to compare their performance in measuring trend over time in inequality for one health indicator. Results Overall, the 11 different measures were more remarkable for their similarities than for their differences. Pairwise measures tended to support the same conclusions as complex summary measures–that is, by identifying same best and worst coverage indicators in each country and indicating similar time trends. Complex measures may be useful to illustrate more nuanced results in countries with a great number of subnational regions. Conclusions When pairwise and complex measures lead to the same conclusions about the state of subnational regional inequality, pairwise measures may be sufficient for reporting inequality. In cases where complex measures are required, mean difference from mean measures can be easily communicated to non-technical audiences.