Template:LognormalDistribution - Revision history

Lisa Hacker: Redirected page to The Lognormal Distribution

2012-08-09T10:01:28Z

Redirected page to The Lognormal Distribution

← Older revision		Revision as of 10:01, 9 August 2012
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	[[~~Category: For Deletion~~]]		#REDIRECT [[The_Lognormal_Distribution]]

Lisa Hacker: Replaced content with 'Category: For Deletion'

2012-07-20T12:19:31Z

Replaced content with 'Category: For Deletion'

← Older revision		Revision as of 12:19, 20 July 2012
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	~~=== The Lognormal Distribution ===~~		[[Category: For Deletion]]

	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> ~~

	~~The lognormal distribution and its characteristics are presented in~~ [[~~The Lognormal Distribution\|The Lognormal Distribution~~]].

	~~<br>~~

Lisa Hacker: /* The Lognormal Distribution */

2012-03-30T21:42:28Z

The Lognormal Distribution

← Older revision		Revision as of 21:42, 30 March 2012
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	</math>		</math>

	<br>where,		<br>where:

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

	The lognormal distribution and its characteristics are presented in~~ detail in the chapter~~ [[The Lognormal Distribution\|The Lognormal Distribution]].		The lognormal distribution and its characteristics are presented in [[The Lognormal Distribution\|The Lognormal Distribution]].

	<br>		<br>

Kate Racaza at 16:02, 12 March 2012

2012-03-12T16:02:10Z

← Older revision		Revision as of 16:02, 12 March 2012
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	=== The Lognormal Distribution ===		=== 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">''~~p''''d''''f~~''</span> of the lognormal distribution is given by:		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}		::<math>\begin{align}

Kate Racaza at 20:10, 11 March 2012

2012-03-11T20:10:25Z

← Older revision		Revision as of 20:10, 11 March 2012
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	===The Lognormal Distribution===		=== 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.		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">''p''''d''''f''</span> of the lognormal distribution is given by:
	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}		::<math>\begin{align}
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	\end{align}		\end{align}
	</math>		</math>
	<br>
	where,		<br>where,

	::<math>\begin{align}		::<math>\begin{align}
	& {\mu'}= \text{mean of the natural logarithms of the times-to-failure} \\		& {\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}		& {\sigma'}= \text{standard deviation of the natural logarithms of the times to failure}
	\end{align}</math>		\end{align}</math>

	The lognormal distribution and its characteristics are presented in ~~more~~ detail in ~~Chapter~~ [[The Lognormal Distribution]].		The lognormal distribution and its characteristics are presented in detail in the chapter [[The Lognormal Distribution\|The Lognormal Distribution]].

	<br>		<br>

Harry Guo: /* The Lognormal Distribution */

2012-02-11T00:00:30Z

The Lognormal Distribution

← Older revision		Revision as of 00:00, 11 February 2012
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	\end{align}</math>		\end{align}</math>

	The lognormal distribution and its characteristics are presented in more detail in [[The Lognormal Distribution ~~\|Chapter 10~~]].		The lognormal distribution and its characteristics are presented in more detail in Chapter [[The Lognormal Distribution]].

	<br>		<br>

Harry Guo: /* The Lognormal Distribution */

2012-02-06T16:31:53Z

The Lognormal Distribution

← Older revision		Revision as of 16:31, 6 February 2012
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	::<math>\begin{align}		::<math>\begin{align}
	& f(t)=\frac{1}{t{\sigma'}\sqrt{2\pi}}e^{-\tfrac{1}{2}(\tfrac{t'-{\mu'}}{\sigma'})^2}\\		& 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 \\		& f(t)\ge 0,t>0,{\sigma'}>0 \\
	& {t'}= \ln (t)		& {t'}= \ln (t)
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	::<math>\begin{align}		::<math>\begin{align}
	& {\mu'}= \text{mean of the natural logarithms of the times-to-failure} \\		& {\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}		& {\sigma'}= \text{standard deviation of the natural logarithms of the times to failure}
	\end{align}</math>		\end{align}</math>

Harry Guo: /* The Lognormal Distribution */

2012-02-06T16:30:12Z

The Lognormal Distribution

← Older revision		Revision as of 16:30, 6 February 2012
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	::<math>\begin{align}		::<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)=\frac{1}{t{\sigma'}\sqrt{2\pi}}e^{-\tfrac{1}{2}(\tfrac{t'-{\mu'}}{\sigma'})^2}\\
	& f(t)\ge 0,t>0,{{\sigma ~~}_{t~~'}}>0 \\		& f(t)\ge 0,t>0,{\sigma'}>0 \\
	& {t'}= \ln (t)		& {t'}= \ln (t)
	\end{align}		\end{align}
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	::<math>\begin{align}		::<math>\begin{align}
	& {\mu'}= \text{mean of the natural logarithms of the times-to-failure} \\		& {\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}		& {\sigma'}}= \text{standard deviation of the natural logarithms of the times to failure}
	\end{align}</math>		\end{align}</math>

Harry Guo: /* The Lognormal Distribution */

2012-02-03T23:12:08Z

The Lognormal Distribution

← Older revision		Revision as of 23:12, 3 February 2012
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	</math>		</math>
	<br>		<br>
	~~:Where~~,		where,

	::<math>\begin{align}		::<math>\begin{align}
	& {\mu'}= \text{mean of the natural logarithms of the times-to-failure} \\		& {\mu'}= \text{mean of the natural logarithms of the times-to-failure} \\

Harry Guo: /* The Lognormal Distribution */

2012-02-03T21:20:30Z

The Lognormal Distribution

← Older revision		Revision as of 21:20, 3 February 2012
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	::<math>\begin{align}		::<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)=\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 \\		& f(t)\ge 0,t>0,{{\sigma }_{t'}}>0 \\
	& {T'}= \ln (t)		& {t'}= \ln (t)
	\end{align}		\end{align}
	</math>		</math>
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	::<math>\begin{align}		::<math>\begin{align}
	& {\mu'}= \text{mean of the natural logarithms of the times-to-failure} \\		& {\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}		& {\sigma_{t'}}= \text{standard deviation of the natural logarithms of the times to failure}
	\end{align}</math>		\end{align}</math>