proportionalityindex: Proportionality deviation index

Description Usage Arguments Details Value References See Also Examples

View source: R/proportionalityindex.R

Description

This function returns the proportionality deviation index of a rule for a claims problem.

Usage

1

Arguments

E

The endowment.

d

The vector of claims.

Rule

A rule: AA, APRO, CE, CEA, CEL, DT, MO, PIN, PRO, RA, Talmud.

Details

Let E> 0 be the endowment to be divided and d the vector of claims with d≥ 0 and such that D=∑ di ≥ E, the sum of claims D exceeds the endowment.

Rearrange the claims from small to large, 0 ≤ d1 ≤...≤ dn. The proportionality deviation index of the rule R for the problem (E,d), denoted by I(R,E,d), is the ratio of the area that lies between the identity line and the cumulative claims-awards curve over the total area under the identity line.

Let d0=0 and R0(E,d)=0. For each k=1,…,n define Xk=(d0+…+dk)/D and Yk=(R0+…+Rk)/E. Then

I(R,E,d)=1-∑ (Xk-X(k-1))(Yk+Y(k-1)) where the sum goes from k=1 to n.

The proportionality deviation index of the proportional rule is zero for all claims problems. In general -1 ≤ I(R,E,d) ≤ 1.

Value

The proportionality deviation index of a rule for a claims problem.

References

Ceriani, L. and Verme, P. (2012). The origins of the Gini index: extracts from Variabilitá e Mutabilitá (1912) by Corrado Gini. The Journal of Economic Inequality, 10(3), 421-443.

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

indexpath, cumulativecurve, lorenzcurve, giniindex, lorenzdominance, PRO.

Examples

1
2
3
4
5
6
E=10
d=c(2,4,7,8)
Rule=AA
proportionalityindex(E,d,Rule)
#The proportionality deviation index of the proportional rule is 0
proportionalityindex(E,d,PRO)

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