Template:Lognormal Distribution Definition: Difference between revisions

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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.  
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.  


The <math>pdf</math> of the lognormal distribution is given by:  
The ''pdf'' of the lognormal distribution is given by:  


::<math>\begin{align}
::<math>\begin{align}

Revision as of 20:34, 29 August 2012

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.

The pdf of the lognormal distribution is given by:

[math]\displaystyle{ \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\gt 0,{\sigma'}\gt 0 \\ & {t'}= \ln (t) \end{align} }[/math]

where [math]\displaystyle{ {\mu'}\,\! }[/math] is the mean of the natural logarithms of the times-to-failure and [math]\displaystyle{ {\sigma'}\,\! }[/math] is the standard deviation of the natural logarithms of the times to failure.

For a detailed discussion of this distribution, see The Lognormal Distribution.