Weibull Distribution Variance Calculator

For a Weibull distribution with shape \( k>0 \) and scale \( \lambda>0 \), the mean is $$ \mu = \lambda\,\Gamma\Bigl(1+\frac{1}{k}\Bigr), $$ and the second moment is $$ E[X^2] = \lambda^2\,\Gamma\Bigl(1+\frac{2}{k}\Bigr). $$ Thus, the variance is $$ \operatorname{Var}(X) = \lambda^2\Bigl[\Gamma\Bigl(1+\frac{2}{k}\Bigr) – \Bigl(\Gamma\Bigl(1+\frac{1}{k}\Bigr)\Bigr)^2\Bigr]. $$

* Enter the parameters \( k > 0 \) and \( \lambda > 0 \). The PDF is $$ f(x; k, \lambda)= \frac{k}{\lambda}\Bigl(\frac{x}{\lambda}\Bigr)^{k-1}\exp\Bigl[-\Bigl(\frac{x}{\lambda}\Bigr)^k\Bigr],\quad x\ge0. $$