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 <span class="texhtml">''pdf''</span> of the lognormal distribution is given by:
-::<math>\begin{align}
-& f(t)=\frac{1}{t{\sigma}'\sqrt{2\pi}}e^{-\tfrac{1}{2}(\tfrac{t'-{\mu'}}{\sigma'})^2}\\
-& f(t)\ge  0,t>0,{\sigma'}>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'}= \text{standard deviation of the natural logarithms of the times to failure}
-\end{align}</math>&nbsp;
-The lognormal distribution and its characteristics are presented in&nbsp;detail in the&nbsp;chapter [[The Lognormal Distribution|The Lognormal Distribution]].
-<br>