Variance of weibull distribution

Question

I want to analyze the variance of weibull (scale,shape) distribution in the range scale to time t. But on solving I am unable to get the closed form expression. Can anyone help.

Answer 1

Variance of Weibull distribution is:

$\sigma^2 = \lambda^2 \ \left\{ \Gamma\left(1 + \displaystyle{\frac{2}{k}}\right) - \left[ \Gamma\left(1 + \displaystyle{\frac{1}{k}}\right) \right]^2 \right\}$

where $\lambda$ is the scale parameter and $k$ is the shape parameter.