On the Relationship Between the Gini Coefficient and Skewness
ABSTRACT Skewness, a measure of the asymmetry of a distribution, is frequently employed to reflect a biologically important property. Another statistic, the Gini coefficient (GC), originally used to measure economic inequality, has been validated in measuring the inequality of biological size distri...
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Wiley
2024-12-01
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| Series: | Ecology and Evolution |
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| Online Access: | https://doi.org/10.1002/ece3.70637 |
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| author | Meng Lian Long Chen Cang Hui Fuyuan Zhu Peijian Shi |
| author_facet | Meng Lian Long Chen Cang Hui Fuyuan Zhu Peijian Shi |
| author_sort | Meng Lian |
| collection | DOAJ |
| description | ABSTRACT Skewness, a measure of the asymmetry of a distribution, is frequently employed to reflect a biologically important property. Another statistic, the Gini coefficient (GC), originally used to measure economic inequality, has been validated in measuring the inequality of biological size distributions. Given that the GC and skewness control overlapping domains and interact with each other, researchers are perplexed by their relationship (varying with the biological [organ, tissue or cell] size distributions) and use both of them together to provide a more complete picture of the data. This study provides analytical forms of the GC for biological size distributions, including two‐parameter Weibull, uniform, normal, two‐parameter lognormal, gamma, three‐parameter Weibull, three‐parameter lognormal, and three‐parameter gamma distributions. Two empirical data sets and simulation data sets were used to clarify the GC–skewness relationships under different distributions. For the aforementioned distributions, the GC–skewness relationships can be divided into three types: (i) for a symmetrical distribution, the skewness is 0, and the GC ranges from 0.56 to 0.58 multiplied by the standard deviation divided by the mean irrespective of its relationship with the skewness; (ii) for an asymmetric distribution with a zero threshold, the GC is a monotonously increasing function of the skewness, and the two measures are equivalent; (iii) for an asymmetric distribution with a non‐zero threshold, the GC is determined by the skewness and an additional correction factor. We showed the differences in improving the accuracy of GC calculations based on small‐sample adjustments among various calculation methods, including the polygon (trapezoidal set) area method and the rotated Lorenz curve method. The present study turns the GC into a property of the distribution and offers a clear understanding for the GC–skewness relationship. This work provides insights into selecting and using the GC to measure inequality in ecological data, facilitating more accurate and meaningful analyses. |
| format | Article |
| id | doaj-art-b8ddb714fc7f4e91bf799a26cbd2e1f3 |
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| issn | 2045-7758 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Wiley |
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| series | Ecology and Evolution |
| spelling | doaj-art-b8ddb714fc7f4e91bf799a26cbd2e1f32025-08-20T02:00:47ZengWileyEcology and Evolution2045-77582024-12-011412n/an/a10.1002/ece3.70637On the Relationship Between the Gini Coefficient and SkewnessMeng Lian0Long Chen1Cang Hui2Fuyuan Zhu3Peijian Shi4Co‐Innovation Centre for Sustainable Forestry in Southern China, State Key Laboratory of Tree Genetics and Breeding, Bamboo Research Institute, College of Life Sciences Nanjing Forestry University Nanjing ChinaCo‐Innovation Centre for Sustainable Forestry in Southern China, State Key Laboratory of Tree Genetics and Breeding, Bamboo Research Institute, College of Life Sciences Nanjing Forestry University Nanjing ChinaDepartment of Mathematical Sciences, Centre for Invasion Biology Stellenbosch University Stellenbosch South AfricaCo‐Innovation Centre for Sustainable Forestry in Southern China, State Key Laboratory of Tree Genetics and Breeding, Bamboo Research Institute, College of Life Sciences Nanjing Forestry University Nanjing ChinaCo‐Innovation Centre for Sustainable Forestry in Southern China, State Key Laboratory of Tree Genetics and Breeding, Bamboo Research Institute, College of Life Sciences Nanjing Forestry University Nanjing ChinaABSTRACT Skewness, a measure of the asymmetry of a distribution, is frequently employed to reflect a biologically important property. Another statistic, the Gini coefficient (GC), originally used to measure economic inequality, has been validated in measuring the inequality of biological size distributions. Given that the GC and skewness control overlapping domains and interact with each other, researchers are perplexed by their relationship (varying with the biological [organ, tissue or cell] size distributions) and use both of them together to provide a more complete picture of the data. This study provides analytical forms of the GC for biological size distributions, including two‐parameter Weibull, uniform, normal, two‐parameter lognormal, gamma, three‐parameter Weibull, three‐parameter lognormal, and three‐parameter gamma distributions. Two empirical data sets and simulation data sets were used to clarify the GC–skewness relationships under different distributions. For the aforementioned distributions, the GC–skewness relationships can be divided into three types: (i) for a symmetrical distribution, the skewness is 0, and the GC ranges from 0.56 to 0.58 multiplied by the standard deviation divided by the mean irrespective of its relationship with the skewness; (ii) for an asymmetric distribution with a zero threshold, the GC is a monotonously increasing function of the skewness, and the two measures are equivalent; (iii) for an asymmetric distribution with a non‐zero threshold, the GC is determined by the skewness and an additional correction factor. We showed the differences in improving the accuracy of GC calculations based on small‐sample adjustments among various calculation methods, including the polygon (trapezoidal set) area method and the rotated Lorenz curve method. The present study turns the GC into a property of the distribution and offers a clear understanding for the GC–skewness relationship. This work provides insights into selecting and using the GC to measure inequality in ecological data, facilitating more accurate and meaningful analyses.https://doi.org/10.1002/ece3.70637adjusted Gini coefficientdiameter at breast heightskewnessWeibull distribution |
| spellingShingle | Meng Lian Long Chen Cang Hui Fuyuan Zhu Peijian Shi On the Relationship Between the Gini Coefficient and Skewness Ecology and Evolution adjusted Gini coefficient diameter at breast height skewness Weibull distribution |
| title | On the Relationship Between the Gini Coefficient and Skewness |
| title_full | On the Relationship Between the Gini Coefficient and Skewness |
| title_fullStr | On the Relationship Between the Gini Coefficient and Skewness |
| title_full_unstemmed | On the Relationship Between the Gini Coefficient and Skewness |
| title_short | On the Relationship Between the Gini Coefficient and Skewness |
| title_sort | on the relationship between the gini coefficient and skewness |
| topic | adjusted Gini coefficient diameter at breast height skewness Weibull distribution |
| url | https://doi.org/10.1002/ece3.70637 |
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