Template:Lognormal distribution standard deviation: Difference between revisions

Latest revision as of 05:15, 13 August 2012

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-===The Standard Deviation===
+#REDIRECT [[Lognormal Distribution Functions]]
-The standard deviation of the lognormal distribution,  <math>{{\sigma }_{T}}</math> , is given by [18]:
-::<math>{{\sigma }_{T}}=\sqrt{\left( {{e}^{2{\mu }'+\sigma _{{{T}'}}^{2}}} \right)\left( {{e}^{\sigma _{{{T}'}}^{2}}}-1 \right)}</math>
-The standard deviation of the natural logarithms of the times-to-failure,  <math>{{\sigma }_{{{T}'}}}</math> , in terms of  <math>\bar{T}</math>  and  <math>{{\sigma }_{T}}</math>  is given by:
-::<math>{{\sigma }_{{{T}'}}}=\sqrt{\ln \left( \frac{\sigma _{T}^{2}}{{{{\bar{T}}}^{2}}}+1 \right)}</math>