Template:Lognormal distribution standard deviation

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The Standard Deviation

The standard deviation of the lognormal distribution, [math]\displaystyle{ {\sigma }} }[/math] , is given by [18]:

[math]\displaystyle{ \sigma =\sqrt{\left( {{e}^{2\mu '+\sigma {{'}^{2}}}} \right)-\left( {{e}^{\sigma {{'}^{2}}}}-1 \right)} }[/math]


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

[math]\displaystyle{ \sigma '=\sqrt{\ln \left( \frac{{{\sigma }^{2}}}{{{{\bar{T}}}^{2}}}+1 \right)} }[/math]