Kumaraswamy Distribution

The Kumaraswamy distribution is a distribution over the interval \((0, 1)\) described by two parameters \(a, b > 0\).

\[Kumaraswamy(x; a, b) = a b x^{a-1} (1 - x^a)^{b-1}\]

Properties

• If \(a=1\) or \(b=1\) or both, the Kumaraswamy and Beta distributions are equivalent.

• Can draw samples using inverse CDF sampling as \(x \sim (1 - u^{1/b})^{1/a}\) where \(u \sim Uniform(0, 1)\).