# Weibull univariate

Suppose ${\displaystyle {\mathbf {x}}=(x_{1},x_{2},\cdots ,x_{n})}$ where ${\displaystyle x_{i}}$ are iid observations from the Weibull distribution with density:

${\displaystyle f(x\mid \lambda ,k)={\frac {k}{\lambda }}\left({\frac {x}{\lambda }}\right)^{k-1}\exp \left(-\left({\frac {x}{\lambda }}\right)^{k}\right),~~~x>0.}$

In the parameterization above, ${\displaystyle k>0}$ is the shape parameter and ${\displaystyle \lambda >0}$ is the scale parameter of the distribution. An alternative parameterization that is sometimes used replaces ${\displaystyle \lambda }$ by ${\displaystyle 1/\beta }$. In medical statistics, the parameterization used replaces ${\displaystyle \lambda }$ by ${\displaystyle b^{k}}$.

## Case 1:

Overall Recommended (OR) prior
In other parameterizations
Recommended prior is of main interest