Template:Lognormal distribution standard deviation: Difference between revisions
Jump to navigation
Jump to search
| Line 1: | Line 1: | ||
===The Standard Deviation=== | ===The Standard Deviation=== | ||
The standard deviation of the lognormal distribution, <math>{{\sigma }}</math> , is given by [[Appendix: Weibull References|18]]]: | The standard deviation of the lognormal distribution, <math>{{\sigma }}</math> , is given by [[Appendix: Weibull References|[18]]]: | ||
::<math>{{\sigma }}=\sqrt{\left( {{e}^{2{\mu }'+\sigma'{2}}} \right)\left( {{e}^{\sigma'{2}}}-1 \right)}</math> | ::<math>{{\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>{{\sigma'}</math> , in terms of <math>\bar{T}</math> and <math>{{\sigma}</math> is given by: | 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^{2}}{{{{\bar{T}}}^{2}}}+1 \right)}</math> | ::<math>\{sigma'}=\sqrt{\ln \left( \frac{\sigma^{2}}{{{{\bar{T}}}^{2}}}+1 \right)}</math> | ||
Revision as of 16:49, 13 February 2012
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]