Weibull Distribution Mode Calculator

For a Weibull distribution with shape parameter \( k>0 \) and scale parameter \( \lambda>0 \), the PDF is given by: $$ f(x; k, \lambda)= \frac{k}{\lambda}\Bigl(\frac{x}{\lambda}\Bigr)^{k-1}\exp\Bigl[-\Bigl(\frac{x}{\lambda}\Bigr)^k\Bigr],\quad x\ge0. $$

The mode is:
– \(0\) if \( k \le 1 \)
– \( x_{\text{mode}} = \lambda\Bigl(\frac{k-1}{k}\Bigr)^{1/k} \) if \( k > 1 \)

* Enter values for \( k \) and \( \lambda \).