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  $${{\sigma }_{T}}$$  is given by:


 * $${{\sigma }_}=\sqrt{\ln \left( \frac{\sigma _{T}^{2}}+1 \right)}$$