This function returns the Gini index of a rule for a claims problem.
giniindex(E, d, Rule)
The vector of claims.
A rule: AA, APRO, CE, CEA, CEL, DT, MO, PIN, PRO, RA, Talmud.
Let E> 0 be the endowment to be divided and d the vector of claims with d≥ 0 and such that D=∑ di ≥ E, the sum of claims D exceeds the endowment.
Rearrange the claims from small to large, 0 ≤ d1 ≤...≤ dn. The Gini index is a number aimed at measuring the degree of inequality in a distribution. The Gini index of the rule R for the problem (E,d), denoted by G(R,E,d), is the ratio of the area that lies between the identity line and the Lorenz curve of the rule over the total area under the identity line.
Let R0(E,d)=0. For each k=0,…,n define Xk=k/n and Yk=(R0+…+Rk)/E. Then
G(R,E,d)=1-∑ (Xk-X(k-1))(Yk+Y(k-1) where the sum goes from k=1 to n.
In general 0≤ G(R,E,d) ≤ 1.
The Gini index of a rule for a claims problem and the Gini index of the vector of claims.
Ceriani, L. and Verme, P. (2012). The origins of the Gini index: extracts from Variabilitá e Mutabilitá (1912) by Corrado Gini. The Journal of Economic Inequality, 10(3), 421-443.
Mirás Calvo, M.A., Núñez Lugilde, I., Quinteiro Sandomingo, C., and Sánchez-Rodríguez, E. (2021). Deviation from proportionality and Lorenz-dominance between the average of awards and the standard rules for claims problems. Working paper 2021-01, ECOBAS.
lorenzcurve, cumulativecurve, proportionalityindex, indexpath, lorenzdominance.
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