```{include} /../core/dataserver/attribute/introducing_tstochastic_attribute/log_uniform_equation.md
```

From the statistical point of view, the mean value of the LogUniform law can then be computed as 
$\mu=\dfrac{x_{\rm max} - x_{\rm min}}{\ln(x_{\rm max}/x_{\rm min})}$ while its variance can be 
written as $\sigma^2=\frac{x_{\rm max}^2-x_{\rm min}^2}{2\ln(x_{\rm max}/x_{\rm min})} - 
\big( \frac{x_{\rm max}-x_{\rm min}}{\ln(x_{\rm max}/x_{\rm min})} \big)^2$. 
By definition, the mode is equal to $x_{\rm min}$. 

```{include} /../core/dataserver/attribute/introducing_tstochastic_attribute/log_uniform_figure.md
```