Template:Lognormal distribution standard deviation

The Standard Deviation
The standard deviation of the lognormal distribution, $${\sigma }_{T}$$, is given by [18]:


 * $${\sigma}_{T} =\sqrt{\left( {{e}^{2\mu '+\sigma {{'}^{2}}}} \right)-\left( {{e}^{\sigma {{'}^{2}}}}-1 \right)}$$

The standard deviation of the natural logarithms of the times-to-failure, $${\sigma}'$$, in terms of  $$\bar{T}$$  and  $${\sigma}$$  is given by:


 * $$\sigma '=\sqrt{\ln \left( \frac{{\sigma}_{T}^{2}}+1 \right)}$$