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

 lorenzcurve R Documentation

## The Lorenz curve

### Description

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

### Usage

```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 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.

### 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.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.

### Examples

```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)
```

ClaimsProblems documentation built on Jan. 12, 2023, 5:13 p.m.