The name is absent

Stata Technical Bulletin

ɪede(ɪ) — / _j,
i=l

fi ⅛g(yt)

The Atkinson indices (Atkinson 1970) are defined by

A(e) = 1 - [y_ede(e)∕nι]

These indices are decomposable but not additively decomposable (Blackorby, Donaldson, and Auersperg 1981):

A(e) = A_w(a) + A_B(a) - [A₁,_y(α)]. [A_s(α)]

where

and

Aw (ɑ) = ¹

fe=l

A_b(o) = 1 -

У de

Social welfare indices (Jenkins 1997) are defined by

W_e = -ɪ- [y_βde(e)]^{1 e}, 0 0 0, e ≠ 1

1 — e

W₁ = log[y_βde(1)]

Each of these indices is an increasing function of a generalized mean of order (1 — e). All the welfare indices are additively
decomposable:

W(e)

= ∑V_kW_k(e)
k=l

The Gini coefficient is given by

G = 1 + (1∕2V) -

(ɪ) ∑(^jv-ⁱ + 1b

∖mJ∖^zJ

where persons are ranked in ascending order of y_B

The Gini coefficient (and the percentile ratios) are not properly decomposable by subgroup into within- and between-group
inequality components.

Sen’s (1976) welfare index is given by

5 = m(1-G)

Syntax

ineqdeco varname [weight] [if exp] [in range] [, bygroup(groupvar) w summ]
fweights and aweights are allowed.