lorenzcurve: The Lorenz curve

In ClaimsProblems: Analysis of Conflicting Claims

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, AV, DT, MO, PIN, PRO, RA, Talmud, RTalmud.
col	The colours. If col=NULL then the sequence of default colors is: c("red", "blue", "green", "yellow", "pink", "orange", "coral4", "darkgray", "burlywood3", "black", "darkorange", "darkviolet").
legend	A logical value. The colour legend is shown if legend=TRUE.

Details

Let N=\{1,\ldots,n\} be the set of claimants, E\ge 0 the endowment to be divided and d\in \mathbb{R}_+^N the vector of claims such that \sum_{i \in N} d_i\ge E.

Rearrange the claims from small to large, 0 \le d_1 \le...\le d_n. The Lorenz curve represents the proportion of the awards given to each subset of claimants by a specific rule \mathcal{R} as a function of the cumulative distribution of population.

The Lorenz curve of a rule \mathcal{R} for the claims problem (E,d) is the polygonal path connecting the n+1 points,

(0,0), \Bigl(\frac{1}{n},\frac{\mathcal{R}_1(E,d)}{E}\Bigr),\dots,\Bigl(\frac{n-1}{n},\frac{\sum_{i=1}^{n-1}\mathcal{R}_i(E,d)}{E}\Bigl),(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. (2023a). Deviation from proportionality and Lorenz-domination for claims problems. Review of Economic Design 27, 439-467.

Mirás Calvo, M.Á., Núñez Lugilde, I., Quinteiro Sandomingo, C., and Sánchez-Rodríguez, E. (2023b). Refining the Lorenz‐ranking of rules for claims problems on restricted domains. International Journal of Economic Theory 19(3), 526-558.

See Also

cumawardscurve, deviationindex, giniindex, 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 April 4, 2025, 2:21 a.m.