On the Relationship Between the Gini Coefficient and Skewness

Area of Science:

• Ecology
• Biostatistics
• Quantitative Biology

Background:

• Skewness measures distribution asymmetry, often reflecting biological properties.
• The Gini coefficient (GC), typically for economic inequality, is used for biological size distribution inequality.
• The interplay between GC and skewness in biological contexts is complex and not fully understood.

Purpose of the Study:

• To derive analytical forms of the Gini coefficient for various biological size distributions.
• To elucidate the relationship between the Gini coefficient and skewness across different distributions.
• To provide a clearer framework for using the Gini coefficient in ecological inequality analyses.

Main Methods:

• Derived analytical forms of the Gini coefficient for distributions including Weibull, uniform, normal, lognormal, and gamma.
• Analyzed empirical and simulation data sets to examine Gini coefficient-skewness relationships.
• Compared small-sample adjustment methods for Gini coefficient calculation, such as the polygon area and rotated Lorenz curve methods.

Main Results:

• Identified three types of Gini coefficient-skewness relationships: symmetrical distributions (skewness=0), asymmetric distributions with zero threshold (GC is a monotonic function of skewness), and asymmetric distributions with non-zero threshold (GC depends on skewness and a correction factor).
• Demonstrated that the Gini coefficient can range from 0.56 to 0.58 times the standard deviation divided by the mean for symmetrical distributions.
• Highlighted differences in accuracy improvements for Gini coefficient calculations using various small-sample adjustment techniques.

Conclusions:

• The Gini coefficient is established as a distributional property, offering a clear understanding of its relationship with skewness.
• The findings facilitate the selection and application of the Gini coefficient for measuring inequality in ecological data.
• This research enables more accurate and meaningful ecological analyses by clarifying Gini coefficient-skewness dynamics.