Dagum distribution for income and wealth modeling
DagumDistribution[p, a, b]
Mean[DagumDistribution[p, a, b]]
→ (b*Gamma[(-1 + a)/a]*Gamma[a^(-1) + p])/Gamma[p]PDF[DagumDistribution[p, a, b], x]
→ Piecewise[{{(a*p*x^(-1 + a*p)*(1 + (x/b)^a)^(-1 - p))/b^(a*p), x > 0}}, 0]Median[DagumDistribution[p, a, b]]
→ b/(-1 + 2^p^(-1))^a^(-1)