A new inequaliy curve I(p) based on the ratio between the lower mean M(p) and the upper mean M+(p) is proposed. By averaging I(p) the new inequality index I is obtained. The index I satisfies the usual properties required to an inequality measure. Being U(p) = 1 - I(p) a ratio between two arithmetic means, the meaning of I(p) is very straightforward. The index I is related to the Gini index R and the Bonferroni index B by the relation: R ≤ B ≤I. In section 6 the curves I(p) and the Lorenz curve L(p) for the N = 14026 personal incomes, regarding the Bank of Italy survey on the household expenditure, are reported.

Zenga, M. (2007). Inequality curve and inequality index based on the ratios between lower and upper arithmetic means. STATISTICA & APPLICAZIONI, 5(1), 3-27.

### Inequality curve and inequality index based on the ratios between lower and upper arithmetic means

#### Abstract

A new inequaliy curve I(p) based on the ratio between the lower mean M(p) and the upper mean M+(p) is proposed. By averaging I(p) the new inequality index I is obtained. The index I satisfies the usual properties required to an inequality measure. Being U(p) = 1 - I(p) a ratio between two arithmetic means, the meaning of I(p) is very straightforward. The index I is related to the Gini index R and the Bonferroni index B by the relation: R ≤ B ≤I. In section 6 the curves I(p) and the Lorenz curve L(p) for the N = 14026 personal incomes, regarding the Bank of Italy survey on the household expenditure, are reported.
##### Scheda breve Scheda completa Scheda completa (DC) Articolo in rivista - Articolo scientifico
Scientifica
inequality, uniformity, lower mean, upper mean
English
3
27
Zenga, M. (2007). Inequality curve and inequality index based on the ratios between lower and upper arithmetic means. STATISTICA & APPLICAZIONI, 5(1), 3-27.
Zenga, M
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Utilizza questo identificativo per citare o creare un link a questo documento: `http://hdl.handle.net/10281/4119`
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