giniindex | R Documentation |

This function returns the Gini index of any rule for a claims problem.

giniindex(E, d, Rule)

`E` |
The endowment. |

`d` |
The vector of claims. |

`Rule` |
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.Á., Núñez Lugilde, I., Quinteiro Sandomingo, C., and Sánchez Rodríguez, E. (2022). Deviation from proportionality and Lorenz-domination for claims problems. Rev Econ Design. doi: 10.1007/s10058-022-00300-y

lorenzcurve, cumawardscurve, deviationindex, indexgpath, lorenzdominance.

E=10 d=c(2,4,7,8) Rule=AA giniindex(E,d,Rule) # The Gini index of the proportional awards coincides with the Gini index of the vector of claims giniindex(E,d,PRO)

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