Template:Lognormal distribution standard deviation - Revision history

Richard House: Redirected page to Lognormal Distribution Functions

2012-08-13T05:15:40Z

Redirected page to Lognormal Distribution Functions

← Older revision		Revision as of 05:15, 13 August 2012
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	~~===The Standard Deviation===~~		#REDIRECT [[Lognormal Distribution Functions]]
	~~The standard deviation of the lognormal distribution, <math>{\sigma }_{T}</math> , is given by~~ [[~~Appendix: Weibull References\|[18]~~]]:

	~~::<math>{\sigma}_{T} =\sqrt{\left( {{e}^{2\mu '+\sigma {{'}^{2}}}} \right)-\left( {{e}^{\sigma {{'}^{2}}}}-1 \right)}</math>~~


	~~The standard deviation of the natural logarithms of the times-to-failure, <math>{\sigma}'</math> , in terms of <math>\bar{T}</math> and <math>{\sigma}</math> is given by:~~

	~~::<math>\sigma '=\sqrt{\ln \left( \frac{{\sigma}_{T}^{2}}{{{{\bar{T}}}^{2}}}+1 \right)}</math>~~

Harry Guo: /* The Standard Deviation */

2012-02-14T23:46:20Z

The Standard Deviation

← Older revision		Revision as of 23:46, 14 February 2012
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	===The Standard Deviation===		===The Standard Deviation===
	The standard deviation of the lognormal distribution, <math>{\sigma }</math> , is given by [[Appendix: Weibull References\|[18]]]:		The standard deviation of the lognormal distribution, <math>{\sigma }_{T}</math> , is given by [[Appendix: Weibull References\|[18]]]:

	::<math>\sigma =\sqrt{\left( {{e}^{2\mu '+\sigma {{'}^{2}}}} \right)-\left( {{e}^{\sigma {{'}^{2}}}}-1 \right)}</math>		::<math>{\sigma}_{T} =\sqrt{\left( {{e}^{2\mu '+\sigma {{'}^{2}}}} \right)-\left( {{e}^{\sigma {{'}^{2}}}}-1 \right)}</math>


	The standard deviation of the natural logarithms of the times-to-failure, <math>{\sigma}'</math> , in terms of <math>\bar{T}</math> and <math>{\sigma}</math> is given by:		The standard deviation of the natural logarithms of the times-to-failure, <math>{\sigma}'</math> , in terms of <math>\bar{T}</math> and <math>{\sigma}</math> is given by:

	::<math>\sigma '=\sqrt{\ln \left( \frac{{{\sigma }^{2}}}{{{{\bar{T}}}^{2}}}+1 \right)}</math>		::<math>\sigma '=\sqrt{\ln \left( \frac{{\sigma}_{T}^{2}}{{{{\bar{T}}}^{2}}}+1 \right)}</math>

Harry Guo: /* The Standard Deviation */

2012-02-13T16:53:40Z

The Standard Deviation

← Older revision		Revision as of 16:53, 13 February 2012
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	===The Standard Deviation===		===The Standard Deviation===
	The standard deviation of the lognormal distribution, <math>{\sigma }}</math> , is given by [[Appendix: Weibull References\|[18]]]:		The standard deviation of the lognormal distribution, <math>{\sigma }</math> , is given by [[Appendix: Weibull References\|[18]]]:

	::<math>\sigma =\sqrt{\left( {{e}^{2\mu '+\sigma {{'}^{2}}}} \right)-\left( {{e}^{\sigma {{'}^{2}}}}-1 \right)}</math>		::<math>\sigma =\sqrt{\left( {{e}^{2\mu '+\sigma {{'}^{2}}}} \right)-\left( {{e}^{\sigma {{'}^{2}}}}-1 \right)}</math>


	The standard deviation of the natural logarithms of the times-to-failure, <math>{\sigma}'</math> , in terms of <math>\bar{T}</math> and <math>{{\sigma}</math> is given by:		The standard deviation of the natural logarithms of the times-to-failure, <math>{\sigma}'</math> , in terms of <math>\bar{T}</math> and <math>{\sigma}</math> is given by:

	::<math>\sigma '=\sqrt{\ln \left( \frac{{{\sigma }^{2}}}{{{{\bar{T}}}^{2}}}+1 \right)}</math>		::<math>\sigma '=\sqrt{\ln \left( \frac{{{\sigma }^{2}}}{{{{\bar{T}}}^{2}}}+1 \right)}</math>

Harry Guo: /* The Standard Deviation */

2012-02-13T16:53:11Z

The Standard Deviation

← Older revision		Revision as of 16:53, 13 February 2012
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	===The Standard Deviation===		===The Standard Deviation===
	The standard deviation of the lognormal distribution, <math>{{\sigma }}</math> , is given by [[Appendix: Weibull References\|[18]]]:		The standard deviation of the lognormal distribution, <math>{\sigma }}</math> , is given by [[Appendix: Weibull References\|[18]]]:

	::<math>\sigma =\sqrt{\left( {{e}^{2\mu '+\sigma {{'}^{2}}}} \right)-\left( {{e}^{\sigma {{'}^{2}}}}-1 \right)}</math>		::<math>\sigma =\sqrt{\left( {{e}^{2\mu '+\sigma {{'}^{2}}}} \right)-\left( {{e}^{\sigma {{'}^{2}}}}-1 \right)}</math>


	The standard deviation of the natural logarithms of the times-to-failure, <math>{{\sigma}'</math> , in terms of <math>\bar{T}</math> and <math>{{\sigma}</math> is given by:		The standard deviation of the natural logarithms of the times-to-failure, <math>{\sigma}'</math> , in terms of <math>\bar{T}</math> and <math>{{\sigma}</math> is given by:

	::<math>\sigma '=\sqrt{\ln \left( \frac{{{\sigma }^{2}}}{{{{\bar{T}}}^{2}}}+1 \right)}</math>		::<math>\sigma '=\sqrt{\ln \left( \frac{{{\sigma }^{2}}}{{{{\bar{T}}}^{2}}}+1 \right)}</math>

Harry Guo: /* The Standard Deviation */

2012-02-13T16:52:50Z

The Standard Deviation

← Older revision		Revision as of 16:52, 13 February 2012
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	The standard deviation of the lognormal distribution, <math>{{\sigma }}</math> , is given by [[Appendix: Weibull References\|[18]]]:		The standard deviation of the lognormal distribution, <math>{{\sigma }}</math> , is given by [[Appendix: Weibull References\|[18]]]:

	::<math>{{\sigma}}=\sqrt{\left( {{e}^{2{\mu }'+{\sigma'}^{2}}} \right)\left( {{e}^{\sigma'}^{2}}}-1 \right)}</math>		::<math>\sigma =\sqrt{\left( {{e}^{2\mu '+\sigma {{'}^{2}}}} \right)-\left( {{e}^{\sigma {{'}^{2}}}}-1 \right)}</math>


	The standard deviation of the natural logarithms of the times-to-failure, <math>{{\sigma'}</math> , in terms of <math>\bar{T}</math> and <math>{{\sigma}</math> is given by:		The standard deviation of the natural logarithms of the times-to-failure, <math>{{\sigma}'</math> , in terms of <math>\bar{T}</math> and <math>{{\sigma}</math> is given by:

	::<math>\{sigma'}=\sqrt{\ln \left( \frac{\sigma^{2}}{{{{\bar{T}}}^{2}}}+1 \right)}</math>		::<math>\sigma '=\sqrt{\ln \left( \frac{{{\sigma }^{2}}}{{{{\bar{T}}}^{2}}}+1 \right)}</math>

Harry Guo: /* The Standard Deviation */

2012-02-13T16:49:56Z

The Standard Deviation

← Older revision		Revision as of 16:49, 13 February 2012
Line 2:		Line 2:
	The standard deviation of the lognormal distribution, <math>{{\sigma }}</math> , is given by [[Appendix: Weibull References\|[18]]]:		The standard deviation of the lognormal distribution, <math>{{\sigma }}</math> , is given by [[Appendix: Weibull References\|[18]]]:

	::<math>{{\sigma}}=\sqrt{\left( {{e}^{2{\mu }'+\sigma'{2}}} \right)\left( {{e}^{\{sigma'}^{2}}}-1 \right)}</math>		::<math>{{\sigma}}=\sqrt{\left( {{e}^{2{\mu }'+{\sigma'}^{2}}} \right)\left( {{e}^{\sigma'}^{2}}}-1 \right)}</math>

Harry Guo: /* The Standard Deviation */

2012-02-13T16:49:04Z

The Standard Deviation

← Older revision		Revision as of 16:49, 13 February 2012
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	===The Standard Deviation===		===The Standard Deviation===
	The standard deviation of the lognormal distribution, <math>{{\sigma }}</math> , is given by [[Appendix: Weibull References\|18]]]:		The standard deviation of the lognormal distribution, <math>{{\sigma }}</math> , is given by [[Appendix: Weibull References\|[18]]]:

	::<math>{{\sigma }}=\sqrt{\left( {{e}^{2{\mu }'+\sigma'{2}}} \right)\left( {{e}^{\sigma'{2}}}-1 \right)}</math>		::<math>{{\sigma}}=\sqrt{\left( {{e}^{2{\mu }'+\sigma'{2}}} \right)\left( {{e}^{\{sigma'}^{2}}}-1 \right)}</math>


	The standard deviation of the natural logarithms of the times-to-failure, <math>{{\sigma'}</math> , in terms of <math>\bar{T}</math> and <math>{{\sigma}</math> is given by:		The standard deviation of the natural logarithms of the times-to-failure, <math>{{\sigma'}</math> , in terms of <math>\bar{T}</math> and <math>{{\sigma}</math> is given by:

	::<math>\sigma'=\sqrt{\ln \left( \frac{\sigma^{2}}{{{{\bar{T}}}^{2}}}+1 \right)}</math>		::<math>\{sigma'}=\sqrt{\ln \left( \frac{\sigma^{2}}{{{{\bar{T}}}^{2}}}+1 \right)}</math>

Harry Guo: /* The Standard Deviation */

2012-02-13T16:48:22Z

The Standard Deviation

← Older revision		Revision as of 16:48, 13 February 2012
Line 1:		Line 1:
	===The Standard Deviation===		===The Standard Deviation===
	The standard deviation of the lognormal distribution, <math>{{\sigma ~~}_{T~~}}</math> , is given by [18]:		The standard deviation of the lognormal distribution, <math>{{\sigma }}</math> , is given by [[Appendix: Weibull References\|18]]]:

	::<math>{{\sigma ~~}_{T~~}}=\sqrt{\left( {{e}^{2{\mu }'+\sigma ~~_{{{T}~~'~~}}^~~{2}}} \right)\left( {{e}^{\sigma ~~_{{{T}~~'~~}}^~~{2}}}-1 \right)}</math>		::<math>{{\sigma }}=\sqrt{\left( {{e}^{2{\mu }'+\sigma'{2}}} \right)\left( {{e}^{\sigma'{2}}}-1 \right)}</math>


	The standard deviation of the natural logarithms of the times-to-failure, <math>{{\sigma ~~}_{{{T}~~'}}}</math> , in terms of <math>\bar{T}</math> and <math>{{\sigma ~~}_{T}~~}</math> is given by:		The standard deviation of the natural logarithms of the times-to-failure, <math>{{\sigma'}</math> , in terms of <math>\bar{T}</math> and <math>{{\sigma}</math> is given by:

	::<math>{{\sigma ~~}_{{{T}~~'~~}}}~~=\sqrt{\ln \left( \frac{\sigma ~~_{T}~~^{2}}{{{{\bar{T}}}^{2}}}+1 \right)}</math>		::<math>\sigma'=\sqrt{\ln \left( \frac{\sigma^{2}}{{{{\bar{T}}}^{2}}}+1 \right)}</math>

Harry Guo: moved Template:Ld standard deviation to Template:Lognormal distribution standard deviation

2012-02-13T16:18:54Z

moved Template:Ld standard deviation to Template:Lognormal distribution standard deviation

← Older revision	Revision as of 16:18, 13 February 2012
(No difference)

Nicolette Young: Created page with '===The Standard Deviation=== The standard deviation of the lognormal distribution, ${{\sigma }_{T}}$ , is given by [18]: :: ${{\sigma }_{T}}=\sqrt{\left( {{e}^{…'$

2012-01-04T18:19:38Z

Created page with '===The Standard Deviation=== The standard deviation of the lognormal distribution, <math>{{\sigma }_{T}}</math> , is given by [18]: ::<math>{{\sigma }_{T}}=\sqrt{\left( {{e}^{…'

New page

===The Standard Deviation===
The standard deviation of the lognormal distribution, <math>{{\sigma }_{T}}</math> , is given by [18]:

::<math>{{\sigma }_{T}}=\sqrt{\left( {{e}^{2{\mu }'+\sigma _{{{T}'}}^{2}}} \right)\left( {{e}^{\sigma _{{{T}'}}^{2}}}-1 \right)}</math>

The standard deviation of the natural logarithms of the times-to-failure, <math>{{\sigma }_{{{T}'}}}</math> , in terms of <math>\bar{T}</math> and <math>{{\sigma }_{T}}</math> is given by:

::<math>{{\sigma }_{{{T}'}}}=\sqrt{\ln \left( \frac{\sigma _{T}^{2}}{{{{\bar{T}}}^{2}}}+1 \right)}</math>

Template:Lognormal distribution standard deviation - Revision history

Richard House: Redirected page to Lognormal Distribution Functions

Harry Guo: /* The Standard Deviation */

Harry Guo: /* The Standard Deviation */

Harry Guo: /* The Standard Deviation */

Harry Guo: /* The Standard Deviation */

Harry Guo: /* The Standard Deviation */

Harry Guo: /* The Standard Deviation */

Harry Guo: /* The Standard Deviation */

Harry Guo: moved Template:Ld standard deviation to Template:Lognormal distribution standard deviation

Nicolette Young: Created page with '===The Standard Deviation=== The standard deviation of the lognormal distribution, {{\sigma }_{T}} , is given by [18]: ::{{\sigma }_{T}}=\sqrt{\left( {{e}^{…'

Nicolette Young: Created page with '===The Standard Deviation=== The standard deviation of the lognormal distribution, ${{\sigma }_{T}}$ , is given by [18]: :: ${{\sigma }_{T}}=\sqrt{\left( {{e}^{…'$