# cumawardscurve: Cumulative awards curve In ClaimsProblems: Analysis of Conflicting Claims

 cumawardscurve R Documentation

## Cumulative awards curve

### Description

The graphical representation of the cumulative curves of a rule (or several rules) with respect to a given rule, for a claims problem.

### Usage

```cumawardscurve(E, d, Rule = PRO, Rules, col = NULL, legend = TRUE)
```

### Arguments

 `E` The endowment. `d` The vector of claims. `Rule` Principal Rule: AA, APRO, CE, CEA, CEL, DT, MO, PIN, PRO, RA, Talmud. By default, Rule = PRO. `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 colours 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 cumulative curve allows us to compare the division recommended by a specific rule R with the division the division recommended by another specific rule S.

The cumulative awards curve of a rule S with respect of a rule R for the claims problem (E,d) is the polygonal path connecting the n+1 points

(0,0) , (R1/E,S1/E) , ((R1+R2)/E , (S1+S2)/E ,… , (1,1).

The cumulative awards curve fully captures the Lorenz ranking of rules: if a rule R Lorenz-dominates a rule S then, for each claims problem, the cumulative curve of R lies above the cumulative curve of S. If R = PRO, the cumulative curve coincides with the cumulative claims-awards curve.

cumulativecurve function of version 0.1.0 returned the cumulative claims-awards curve with respect to the proportional rule.

### Value

The graphical representation of the cumulative curves 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

### See Also

deviationindex, indexgpath, lorenzcurve, giniindex, lorenzdominance, allrules.

### Examples

```E=10
d=c(2,4,7,8)
Rule=PRO
Rules=c(AA,RA,Talmud,CEA,CEL)
cumawardscurve(E,d,Rule,Rules)
```

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