Template:Lognormal distribution standard deviation

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


 * $$\sigma =\sqrt{\left( {{e}^{2\mu '+\sigma {{'}^{2}}}} \right)-\left( {{e}^{\sigma {{'}^{2}}}}-1 \right)}$$

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


 * $$\sigma '=\sqrt{\ln \left( \frac+1 \right)}$$