Fig. 2: Illustration of the distribution of major depressive disorder symptom combinations and analysis of inequality via Lorenz curves.

a Distribution of symptom presentations in patients with major depressive disorder as reported by Zimmerman et al.⁴ and Park et al.⁵ (data extracted from their published tables). b Lorenz curves for the empirical distributions shown in (a). Curve colors are matched between panels. In this case, the Lorenz curve demonstrates the proportion of symptom combinations \(\left( {P_{{\mathrm{Combinations}}}} \right)\) that account for at least \(P_{{\mathrm{Samples}}}\) proportion of observed presentations in the datasets. The diagonal (black) line represents the line of perfect equality, which would occur only if all symptom combinations accounted for the same proportion of observed presentations. The closer a Lorenz curve is to the upper corner, the more inequality exists in the abundance distribution, which in this case would indicate greater homogeneity of symptom presentations. Geometric calculation of the Gini coefficient and Pietra indices is also demonstrated. The Gini index is the ratio of (A) the area between the Lorenz curve and the line of perfect equality to (B) the total area above the Lorenz curve. The Pietra index is the maximum distance from the Lorenz curve to the line of perfect equality, and represents the proportion of observations that would need to be transferred from the most common to the least common symptom combinations in order to reach the line of perfect equality.