Kumaraswamy Distribution Mode Calculator
For the Kumaraswamy distribution with parameters \(a\) and \(b\), the PDF is given by: $$ f(x; a, b) = a\,b\, x^{a-1}\,(1 – x^a)^{b-1},\quad 0\le x\le 1. $$
* Enter parameters \(a>0\) and \(b>0\).
– If \(a>1\) and \(b>1\), the interior mode is
$$ x_{\mathrm{mode}} = \Bigl(\frac{a-1}{a\,b – 1}\Bigr)^{1/a}. $$
– Otherwise, the mode is at a boundary: \(0\) (if \(a\le1\)) or \(1\) (if \(b\le1\)).
Step 1: Enter Parameters
e.g., 2
e.g., 3
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