# lorenzcurve: The Lorenz curve In ClaimsProblems: Analysis of Conflicting Claims

## Description

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

## Usage

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

## Arguments

 `E` The endowment. `d` The vector of claims. `Rules` The rules: AA, APRO, CE, CEA, CEL, DT, MO, PIN, PRO, RA, Talmud. `col` The colors. 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 color legend is shown if legend=TRUE.

## Details

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.

## Value

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

## References

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

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.

 ```1 2 3 4 5``` ```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) ```