cumulativecurve: Cumulative claims-awards curve

Description Usage Arguments Details Value References See Also Examples

View source: R/cumulativecurve.R

Description

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

Usage

1
cumulativecurve(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 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'.

Value

The graphical representation of the cumulative claims-awards 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.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.

See Also

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

Examples

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

ClaimsProblems documentation built on April 7, 2021, 9:07 a.m.