Template:LognormalDistribution: Difference between revisions

Latest revision as of 10:01, 9 August 2012

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-===The Lognormal Distribution===
+#REDIRECT [[The_Lognormal_Distribution]]
-The lognormal distribution is commonly used for general reliability analysis, cycles-to-failure in fatigue, material strengths and loading variables in probabilistic design.
-When the natural logarithms of the times-to-failure are normally distributed, then we say that the data follow the lognormal distribution.
-<br>
-The <math>pdf</math> of the lognormal distribution is given by:
-::<math>\begin{align}
-& f(t)=\frac{1}{t{\sigma}_{t'}\sqrt{2\pi}}e^{-\tfrac{1}{2}(\tfrac{t'-{\mu'}}{\sigma_{t'}})^2}\\
-& f(t)\ge  0,t>0,{{\sigma }_{t'}}>0 \\
-& {t'}=  \ln (t)
-\end{align}
-</math>
-<br>
-where,
-::<math>\begin{align}
- &  {\mu'}= \text{mean of the natural logarithms of the times-to-failure} \\
-&  {\sigma_{t'}}= \text{standard deviation of the natural logarithms of the times to failure}
-\end{align}</math>
-The lognormal distribution and its characteristics are presented in more detail in [[The Lognormal Distribution |Chapter 10]].
-<br>