Table 2. The parametric theoretical models considered in our empirical analyses.

Rows 1-9: Lorenz curve models from distributional origin. Rows 10-17: Functional forms proposed to model Lorenz curves. Model 14 is recognized as a family of Lorenz curves but not proposed as a Lorenz curve specifically. As this family is the most general form of the specific Lorenz curve that [62] propose, we use it as a four-parameter Lorenz curve (see [63, 64, 65, 66, 67]). η denotes the cumulative percentage of income, u denotes the cumulative percentage of the population. Φ() is the cumulative distribution function of the standard normal distribution, G() is the incomplete gamma function ratio, B() is the lower incomplete beta function ratio as defined in the SI Notation Preface. Details on parameter restrictions are given in SI, Section 1.

Originates from	Lorenz curve η(u)
1. Pareto distribution	1 – (1 – u)1 – 1/α
2. Lognormal distribution	Φ(Φ–1 (u) – σ)
3. Gamma distribution	G(G–1(u; σ); σ + 1)
4. Weibull distribution	$G\left(-\log (1-u);\frac{1}{\alpha }+1\right)$
5. Gen. Gamma distr.	$G\left(G^{-1}(u;p);p+\frac{1}{a}\right)$
6. Dagum distribution	$B\left(u^{1/q};q+\frac{1}{a},1-\frac{1}{a}\right)$
7. Singh-Maddala distr.	$B(1-{(1-u)}^{1/q};1+\frac{1}{a},q-\frac{1}{a})$
8. GB1 distribution	$B\left(B^{-1}(u;p,q);p+\frac{1}{a},q\right)$
9. GB2 distribution	$B\left(B^{-1}(u;p,q);p+\frac{1}{a},q-\frac{1}{a}\right)$
10. Kakwani/Podder [68]	ue –β(1–u)
11. Rasche et al. [69]	(1 – (1 – u)α)1/β
12. Ortega et al. [26]	uα(1 – (1 – u)β)
13. Chotikapanich [70]	$\frac{e^{ku}-1}{e^k-1}$
14. Sarabia et al. [62]	uα + γ[1 – a(1 – u)β]γ
15. Abdalla/Hassan [71]	uα (1 – (1 – u)δeβu)
16. Rhode [72]	$u\cdot \frac{\beta -1}{\beta -u}$
17. Wang et al. [73]	δuα[1 – (1 – u)β] + (1 – δ)[1 – (1 – u)β1]ν