lorenzcurve | R Documentation |

This function returns the Lorenz curve of any rule for a claims problem.

lorenzcurve(E, d, Rules, col = NULL, legend = TRUE)

`E` |
The endowment. |

`d` |
The vector of claims. |

`Rules` |
The rules: AA, APRO, CE, CEA, CEL, DT, MO, PIN, PRO, RA, Talmud. |

`col` |
The colours. If col=NULL then the sequence of default colors is: c("red", "blue", "green", "yellow", "pink", "coral4", "darkgray", "burlywood3", "black", "darkorange", "darkviolet"). |

`legend` |
A logical value. The colour legend is shown if legend=TRUE. |

Let *E> 0* be the endowment to be divided and *d* the vector of claims
with *d≥ 0* and such that the sum of claims *D=∑ di* exceeds the endowment.

Rearrange the claims from small to large, *
0 ≤ d1 ≤...≤ dn*. The Lorenz curve represents the proportion of the awards given to each subset of claimants by a specific rule *R* as a function of the
cumulative distribution of population.

The Lorenz curve of a rule *R* for the claims problem *(E,d)* is the polygonal path connecting the *n+1* points

*
(0,0) , (1/n,R1(E,d)/E) , (2/n , (R1(E,d)+R2(E,d))/E ,… , (1,1)*

Basically, it represents the cumulative percentage of the endowment assigned by the rule to each cumulative percentage of claimants.

The graphical representation of the Lorenz curve of a rule (or several rules) for a claims problem.

Lorenz, M. O. (1905). Methods of measuring the concentration of wealth. Publications of the American statistical association, 9(70), 209-219.

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

giniindex, cumawardscurve, deviationindex, indexgpath, lorenzdominance.

E=10 d=c(2,4,7,8) Rules=c(AA,RA,Talmud,CEA,CEL) col=c("red","blue","green","yellow","pink") lorenzcurve(E,d,Rules,col)

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