View source: R/cumawardscurve.R

cumawardscurve | R Documentation |

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

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

`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. |

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.

The graphical representation of the cumulative curves 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

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

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

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