Description Usage Arguments Details Value References See Also Examples

View source: R/cumulativecurve.R

This function returns the cumulative claims-awards curve of a rule for a claims problem.

1 | ```
cumulativecurve(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 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. |

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 claims-awards curve allows us
to compare the division recommended by a specific rule *R* with the division that preserves the proportions of the
claims, the proportional rule.

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

*
(0,0) , (d1/D,R1(E,d)/E) , ((d1+d2)/D , (R1(E,d)+R2(E,d))/E ,… , (1,1).*

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

The cumulative claims-awards curve fully captures the Lorenz ranking of rules:
if a rule *R* Lorenz-dominates a rule *R'* then, for each claims problem, the cumulative claims-awards curve of *R*
lies above the cumulative curve of *R'*.

The graphical representation of the cumulative claims-awards 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.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.

proportionalityindex, indexpath, lorenzcurve, giniindex, lorenzdominance, PRO.

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