Weighted inequality indicators

weighted_inequality_indicators.jl

##### Atkinson index #####
"""
    atkinson(v, w, ϵ)
Computes the weighted Atkinson index given an inequality adversion parameter ϵ.
"""
function wtd_atkinson(v::Array{<:Real,1}, w::Array{<:Real,1}, ϵ::Real) ::Float64
 
    v = v/Statistics.mean(v)
    w = w/sum(w)
 
    if ϵ == 1
        w = w[v .!= 0]
        v = v[v .!= 0]
        
        return 1 - (prod(exp.(w.*log.(v)))/sum(v .* w/sum(w)) )
    elseif ϵ < 1
        return 1-(sum(((v/sum(v.*w/sum(w))).^(1-ϵ)).*w/sum(w))).^(1/(1-ϵ))
    else 
        w = w[v .!= 0]
        v = v[v .!= 0]
        
        return 1-(sum(((v/sum(v.*w/sum(w))).^(1-ϵ)).*w/sum(w))).^(1/(1-ϵ))
    end