Template:Lognormal Distribution Definition - Revision history

Richard House at 21:45, 21 September 2012

2012-09-21T21:45:58Z

← Older revision		Revision as of 21:45, 21 September 2012
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	& f(t)\ge 0,t>0,{\sigma'}>0 \\		& f(t)\ge 0,t>0,{\sigma'}>0 \\
	& {t'}= \ln (t)		& {t'}= \ln (t)
	\end{align}		\end{align}\,\!
	</math>		</math>

Richard House at 20:34, 29 August 2012

2012-08-29T20:34:52Z

← Older revision		Revision as of 20:34, 29 August 2012
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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}

Richard House at 03:01, 22 August 2012

2012-08-22T03:01:41Z

← Older revision		Revision as of 03:01, 22 August 2012
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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 <~~span class="texhtml"~~>''pdf''</~~span~~> of the lognormal distribution is given by:		The <math>pdf</math> of the lognormal distribution is given by:

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

	where <math>{\mu'}</math> is the mean of the natural logarithms of the times-to-failure and <math>{\sigma'}</math> is the standard deviation of the natural logarithms of the times to failure.		where <math>{\mu'}\,\!</math> is the mean of the natural logarithms of the times-to-failure and <math>{\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]].		For a detailed discussion of this distribution, see [[The Lognormal Distribution]].

Richard House at 01:40, 8 August 2012

2012-08-08T01:40:54Z

← Older revision		Revision as of 01:40, 8 August 2012
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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.

	~~<br>~~The <span class="texhtml">''pdf''</span> of the lognormal distribution is given by:		The <span class="texhtml">''pdf''</span> of the lognormal distribution is given by:

	::<math>\begin{align}		::<math>\begin{align}
Line 10:		Line 10:
	</math>		</math>

	~~<br>~~where <math>{\mu'}</math> is the mean of the natural logarithms of the times-to-failure and <math>{\sigma'}</math> is the standard deviation of the natural logarithms of the times to failure.		where <math>{\mu'}</math> is the mean of the natural logarithms of the times-to-failure and <math>{\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]].		For a detailed discussion of this distribution, see [[The Lognormal Distribution]].

Lisa Hacker: Created page with 'The lognormal distribution is commonly used for general reliability analysis, cycles-to-failure in fatigue, material strengths and loading variables in probabilistic design. When…'

2012-08-07T03:14:34Z

Created page with 'The lognormal distribution is commonly used for general reliability analysis, cycles-to-failure in fatigue, material strengths and loading variables in probabilistic design. When…'

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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.

<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>{\mu'}</math> is the mean of the natural logarithms of the times-to-failure and <math>{\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]].