Kumaraswamy continuous distribution on the unit interval
KumaraswamyDistribution[α, β]
Mean[KumaraswamyDistribution[α, β]]
→ β*Beta[β, 1 + α^(-1)]PDF[KumaraswamyDistribution[α, β], x]
→ Piecewise[{{x^(-1 + α)*(1 - x^α)^(-1 + β)*α*β, 0 < x < 1}}, 0]CDF[KumaraswamyDistribution[α, β], x]
→ Piecewise[{{1 - (1 - x^α)^β, 0 < x < 1}, {1, x >= 1}}, 0]