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 [[Appendix: Weibull References|[18]]]:
-::<math>{\sigma}_{T} =\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>{\sigma}'</math> , in terms of  <math>\bar{T}</math>  and  <math>{\sigma}</math>  is given by:
-::<math>\sigma '=\sqrt{\ln \left( \frac{{\sigma}_{T}^{2}}{{{{\bar{T}}}^{2}}}+1 \right)}</math>