Estimation of the Gini coefficient for the lognormal distribution of income using the Lorenz curve

Darkwah, Kwasi A.; Nortey, Ezekiel N. N.; Lotsi, Anani

doi:10.1186/s40064-016-2868-z

Cited by 12 publications

(11 citation statements)

References 14 publications

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“…Moreover, from an extensive comparison of several different distributions proposed as models for empirical income data, such as including gamma and beta types of distributions and others [ 35 ], the lognormal distribution was found to surpass the usage of other distributions in many practical applications (see from page 126). More recently, statistical testing of 15 different income distributions in Ghana, Africa, showed no significant deviation from log-normal distributions [ 29 ], which agrees with the present results of curve fitting. Of note, the present approach to analyze the distributions of Gini indices can be transferred easily to the above-mentioned indices.…”

Section: Discussionsupporting

confidence: 87%

“…A second focus of the present analysis was amending the ambiguity of the classical Gini index. Despite the fact that the Gini coefficient has been judged as one of the most efficient measurements of income inequality in the world [ 29 ], it is known to suffer from several shortcomings. As a main weakness, its incapability of differentiating different kinds of inequalities has been highlighted [ 30 ].…”

Section: Discussionmentioning

confidence: 99%

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A data science based standardized Gini index as a Lorenz dominance preserving measure of the inequality of distributions

Ultsch

Lötsch

2017

PLoS ONE

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The Gini index is a measure of the inequality of a distribution that can be derived from Lorenz curves. While commonly used in, e.g., economic research, it suffers from ambiguity via lack of Lorenz dominance preservation. Here, investigation of large sets of empirical distributions of incomes of the World’s countries over several years indicated firstly, that the Gini indices are centered on a value of 33.33% corresponding to the Gini index of the uniform distribution and secondly, that the Lorenz curves of these distributions are consistent with Lorenz curves of log-normal distributions. This can be employed to provide a Lorenz dominance preserving equivalent of the Gini index. Therefore, a modified measure based on log-normal approximation and standardization of Lorenz curves is proposed. The so-called UGini index provides a meaningful and intuitive standardization on the uniform distribution as this characterizes societies that provide equal chances. The novel UGini index preserves Lorenz dominance. Analysis of the probability density distributions of the UGini index of the World’s counties income data indicated multimodality in two independent data sets. Applying Bayesian statistics provided a data-based classification of the World’s countries’ income distributions. The UGini index can be re-transferred into the classical index to preserve comparability with previous research.

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Section: Discussionsupporting

confidence: 87%

Section: Discussionmentioning

confidence: 99%

A data science based standardized Gini index as a Lorenz dominance preserving measure of the inequality of distributions

Ultsch

Lötsch

2017

PLoS ONE

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“…Using well-developed measures of disparity to evaluate its impact on AKI risk should be assessed in future investigations (e.g., the Gini coefficient commonly used measure of inequality to detect the income distribution of residents in each country). 44 …”

Section: Methodsmentioning

confidence: 99%

Acute Kidney Injury Risk Assessment: Differences and Similarities Between Resource-Limited and Resource-Rich Countries

Kashani

Macedo

Burdmann

et al. 2017

Kidney International Reports

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The incidence of acute kidney injury (AKI) among acutely ill patients is reportedly very high and has vexing consequences on patient outcomes and health care systems. The risks and impact of AKI differ between developed and developing countries. Among developing countries, AKI occurs in young individuals with no or limited comorbidities, and is usually due to environmental causes, including infectious diseases. Although several risk factors have been identified for AKI in different settings, there is limited information on how risk assessment can be used at population and patient levels to improve care in patients with AKI, particularly in developing countries where significant health disparities may exist. The Acute Disease Quality Initiative consensus conference work group addressed the issue of identifying risk factors for AKI and provided recommendations for developing individualized risk stratification strategies to improve care. We proposed a 5-dimension, evidence-based categorization of AKI risk that allows clinicians and investigators to study, define, and implement individualized risk assessment tools for the region or country where they practice. These dimensions include environmental, socioeconomic and cultural factors, processes of care, exposures, and the inherent risks of AKI. We provide examples of these risks and describe approaches for risk assessments in the developing world. We anticipate that these recommendations will be useful for health care providers to plan and execute interventions to limit the impact of AKI on society and each individual patient. Using a modified Delphi process, this group reached consensus regarding several aspects of AKI risk stratification.

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“…The Gini coefficient of inequality was computed for the lognormal distribution [73] of income. Using its shape parameter s (see below) the Gini coefficient was computed as G = erfc(−s/2) − 1; erfc is the complementary error function [74,75]. The probability density function of the lognormal distribution is defined for positive x from a location parameter m and a shape parameter s > 0:…”

Section: General Computationsmentioning

confidence: 99%

Affordability of Decentralized Wastewater Systems: A Case Study in Integrated Planning from INDIA

Brunner

Starkl

Kazmi

et al. 2018

Water

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Based on experiences about the planning of decentralized wastewater treatment systems for slums of two rural towns in India, the paper asks to what extent affordability for the future users may impede the realization of other sustainability goals. The planning aimed at ensuring economic, social, and environmental sustainability. To this end the planning process promoted the participation of stakeholders and it was supplemented by an in-depth analysis (using novel methods) of the socio-economic situation of the future users. In particular, an approach towards estimating willingness to pay from small samples was developed. Taking all this information into account, planning identified a well-established technology that it is inexpensive, robust, and easy to maintain. The experiences of this planning process may generalize to other developing countries seeking socially acceptable low cost solutions with reasonable pollution reduction for resolving the sanitation crisis.

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Estimation of the Gini coefficient for the lognormal distribution of income using the Lorenz curve

Cited by 12 publications

References 14 publications

A data science based standardized Gini index as a Lorenz dominance preserving measure of the inequality of distributions

A data science based standardized Gini index as a Lorenz dominance preserving measure of the inequality of distributions

Acute Kidney Injury Risk Assessment: Differences and Similarities Between Resource-Limited and Resource-Rich Countries

Affordability of Decentralized Wastewater Systems: A Case Study in Integrated Planning from INDIA

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