Kumaraswamy Distribution Mode Calculator

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

For \(a>1\) and \(b>1\): $$ x_{\mathrm{mode}} = \Bigl(\frac{a-1}{a\,b-1}\Bigr)^{1/a}. $$

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