atkinson(v, ϵ)

Compute the Atkinson Index of a vector v at a specified inequality aversion parameter ϵ.

Examples

julia> using Inequality
julia> atkinson([8, 5, 1, 3, 5, 6, 7, 6, 3], 1.2)
0.1631765870035865

atkinson(v, w, ϵ)

Compute the weighted Atkinson Index of a vector v at a specified inequality aversion parameter ϵ, using weights given by a weight vector w.

Weights must not be negative, missing or NaN. The weights and data vectors must have the same length.

Examples

julia> using Inequality
julia> atkinson([8, 5, 1, 3], [0.1,0.5,0.3,0.8], 1.2)
0.1681319821792493

gini(v)

Compute the Gini Coefficient of a vector v .

Examples

julia> using Inequality
julia> gini([8, 5, 1, 3, 5, 6, 7, 6, 3])
0.2373737373737374

gini(v, w)

Compute the weighted Gini Coefficient of a vector v using weights given by a weight vector w.

Weights must not be negative, missing or NaN. The weights and data vectors must have the same length.

Examples

julia> using Inequality
julia> gini([8, 5, 1, 3, 5, 6, 7, 6, 3], collect(0.1:0.1:0.9))
0.20652395514780775

lorenz(v)

Compute the relative Lorenz Curve of a vector v .

Returns two vectors. The first one contains the cumulative proportion of people. The second contains the cumulative share of income earned.

Examples

julia> using Inequality
julia> lorenz_curve([8, 5, 1, 3, 5, 6, 7, 6, 3])
([0.0, 0.1111111111111111, 0.2222222222222222, 0.3333333333333333, 0.4444444444444444, 0.5555555555555556, 0.6666666666666666, 0.7777777777777778, 0.8888888888888888, 1.0], 
│ [0.0, 0.022727272727272728, 0.09090909090909091, 0.1590909090909091, 0.2727272727272727, 0.38636363636363635, 0.5227272727272727, 0.6590909090909091, 0.8181818181818182, 1.0])

lorenz(v, w) Compute the weighted Lorenz Curve of a vector v using weights given by a weight vector w.

Weights must not be negative, missing or NaN. The weights and data vectors must have the same length.

Returns two vectors. The first one contains the cumulative proportion of weighted people. The second contains the cumulative share of income earned.

Examples

julia> using Inequality
julia> lorenz_curve([8, 5, 1, 3, 5, 6, 7, 6, 3], collect(0.1:0.1:0.9))
([0.0, 0.06666666666666667, 0.08888888888888889, 0.13333333333333333, 0.2222222222222222, 0.3333333333333333, 0.5333333333333333, 0.6666666666666666, 0.8444444444444444, 1.0],
[0.0, 0.013761467889908256, 0.05045871559633028, 0.0963302752293578, 0.1513761467889908, 0.2660550458715596, 0.38990825688073394, 0.555045871559633, 0.7752293577981653, 1.0])

mld(v)

Compute the Mean log deviation of a vector v.

Examples

julia> using Inequality
julia> mld([8, 5, 1, 3, 5, 6, 7, 6, 3])
0.1397460530936332

mld(v, w)

Compute the weighted Mean log deviation of a vector v using weights given by a weight vector w.

Weights must not be negative, missing or NaN. The weights and data vectors must have the same length.

Examples

julia> using Inequality
julia> mld([8, 5, 1, 3, 5, 6, 7, 6, 3], collect(0.1:0.1:0.9))
0.10375545537468206

gen_entropy(v, α)

Compute the Generalized Entropy Index of a vector `v` at a specified parameter `α`.

Examples

julia> using Inequality
julia> gen_entropy([8, 5, 1, 3, 5, 6, 7, 6, 3], 2)
0.09039256198347094

gen_entropy(v, w, α)

Compute the Generalized Entropy Index of a vector v, using weights given by a weight vector w at a specified parameter α.

Weights must not be negative, missing or NaN. The weights and data vectors must have the same length.

Examples

julia> using Inequality
julia> gen_entropy([8, 5, 1, 3, 5, 6, 7, 6, 3], collect(0.1:0.1:0.9), 2)
0.0709746654322026

watts(v, k)

Compute the Watts Poverty Index of a vector `v` at a specified absolute 
poverty line `k`.

Examples

julia> using Inequality
julia> watts([8, 5, 1, 3, 5, 6, 7, 6, 3], 4)
0.217962056224828

watts(v, w, α)

Compute the Watts Poverty Index of a vector v at a specified absolute poverty line α, using weights given by a weight vector w.

Weights must not be negative, missing or NaN. The weights and data vectors must have the same length.

Examples

julia> using Inequality
julia> watts([8, 5, 1, 3, 5, 6, 7, 6, 3], collect(0.1:0.1:0.9), 4)
0.17552777833850716

theil(v)

Compute the Theil Index of a vector `v`.

Examples

julia> using Inequality
julia> theil([8, 5, 1, 3, 5, 6, 7, 6, 3])
0.10494562214323544

theil(v, w)

Compute the Theil Index of a vector v, using weights given by a weight vector w.

Weights must not be negative, missing or NaN. The weights and data vectors must have the same length.

Examples

julia> using Inequality
julia> theil([8, 5, 1, 3, 5, 6, 7, 6, 3], collect(0.1:0.1:0.9))
0.08120013911680612

fgt(v, α, z)

Compute the Foster–Greer–Thorbecke Index of a vector v at a specified α and a given poverty threshold z.

Examples

julia> using Inequality
julia> fgt([8, 5, 1, 3, 5, 6, 7, 6, 3], 2, 4)
0.0763888888888889

fgt(v, w, α, z)

Compute the Foster–Greer–Thorbecke Index of a vector v at a specified α and a given poverty threshold z, using weights given by a weight vector w.

Weights must not be negative, missing or NaN. The weights and data vectors must have the same length.

Examples

julia> using Inequality
julia> fgt([8, 5, 1, 3, 5, 6, 7, 6, 3], collect(0.1:0.1:0.9), 2, 4)
0.05555555555555555

headcount(v, z)

Compute the Headcount Ratio of a vector v at a specified poverty threshold z.

Examples

julia> using Inequality
julia> headcount([8, 5, 1, 3, 5, 6, 7, 6, 3], 4)
0.3333333333333333

headcount(v, w, z)

Compute the Headcount Ratio of a vector v at a specified poverty threshold z, using weights given by a weight vector w.

Weights must not be negative, missing or NaN. The weights and data vectors must have the same length.

Examples

julia> using Inequality
julia> headcount([8, 5, 1, 3, 5, 6, 7, 6, 3], [0.1,0.5,0.3,0.8,0.1,0.5,0.3,0.8,0.2], 4)
0.36111111111111116

poverty_gap(v, z)

Compute the Poverty Gap of a vector v at a specified poverty threshold z.

Examples

julia> using Inequality
julia> poverty_gap([8, 5, 1, 3, 5, 6, 7, 6, 3], 4)
0.1388888888888889

poverty_gap(v, w, z)

Compute the Poverty Gap of a vector v at a specified poverty threshold z, using weights given by a weight vector w.

Weights must not be negative, missing or NaN. The weights and data vectors must have the same length.

Examples

julia> using Inequality
julia> poverty_gap([8, 5, 1, 3, 5, 6, 7, 6, 3], [0.1,0.5,0.3,0.8,0.1,0.5,0.3,0.8,0.2], 4)
0.13194444444444445