Weibull Distribution - Examples - Revision history

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	[[~~Category: For Deletion~~]]		#REDIRECT [[Weibull%2B%2B_Examples]]

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2012-08-07T05:24:13Z

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Chris Kahn: moved Weibull Distribution Examples to Weibull Distribution - Examples: Need the original page name for a smaller list of examples.

2012-08-07T01:12:04Z

moved Weibull Distribution Examples to Weibull Distribution - Examples: Need the original page name for a smaller list of examples.

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Richard House at 01:51, 6 August 2012

2012-08-06T01:51:31Z

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	[[Category:Life Data Analysis Reference]]		[[Category:Life Data Analysis Reference]]
	~~{{RS Copyright}}~~

Pantelis at 17:59, 2 March 2011

2011-03-02T17:59:17Z

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	{{TOC right}}		{{UConstruction}}



			{{TOC right}}

	=General Examples=		=General Examples=

Pantelis: Protected "Weibull Distribution Examples" ([edit=autoconfirmed] (indefinite) [move=autoconfirmed] (indefinite))

2011-02-28T21:34:01Z

Protected "Weibull Distribution Examples" ([edit=autoconfirmed] (indefinite) [move=autoconfirmed] (indefinite))

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Pengying niu: /* SUBSUBSECTION */

2011-02-28T21:23:24Z

SUBSUBSECTION

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	Published Results for Example 19 Published results (using probability plotting):\		Published Results for Example 19 Published results (using probability plotting):\

	<math> \hat{\beta }=3.0,~~\text{ \ }~~\hat{\eta }=1,220,~~\text{ \ }~~\hat{ \gamma }=-300 </math>		<math> \hat{\beta }=3.0,\hat{\eta }=1,220,\hat{ \gamma }=-300 </math>


	====SUBSUBSECTION====		====SUBSUBSECTION====

Pengying niu: /* SUBSUBSECTION */

2011-02-28T21:22:41Z

SUBSUBSECTION

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	Weibull++\ computed parameters for maximum likelihood are:		Weibull++\ computed parameters for maximum likelihood are:

	~~<math>~~		<math> \hat{\beta }=1.0584 </math>
	{\|
	\|-		<math> \hat{\eta }=26,296 </math>
	\| <math> \hat{\beta }=1.0584 </math>
	\|-
	\| <math> \hat{\eta }=26,296 </math>
	\|}
	~~</math>~~
	Weibull++ computed 95\\ FM\ confidence limits on the parameters:		Weibull++ computed 95\\ FM\ confidence limits on the parameters:

	~~<math>~~
	{\|		<math> \hat{\beta }=\left\{ 0.6441,\text{ }1.7394\right\} </math>
	\|-		<math> \hat{\eta }=\left\{ 10,552,\text{ }65,532\right\} </math>
	\| <math> \hat{\beta }=\left\{ 0.6441,\text{ }1.7394\right\} </math>
	\|-
	\| <math> \hat{\eta }=\left\{ 10,552,\text{ }65,532\right\} </math>
	\|}
	~~</math>~~
	Weibull++ computed/variance covariance matrix:		Weibull++ computed/variance covariance matrix:

	<math> \left[ \begin{array}{ccc} \hat{Var}\left( \hat{\beta }\right) =0.0720 ~~\|\| \|\|~~ \hat{Cov}( \hat{\beta },\hat{\eta })=-2,664.40		<math> \left[ \begin{array}{ccc} \hat{Var}\left( \hat{\beta }\right) =0.0720 & \hat{Cov}( \hat{\beta },\hat{\eta })=-2,664.40 \\
	\|-
	~~\| \|\| \|\|~~		\hat{Cov}(\hat{\beta },\hat{\eta })=-2,664.40 & \hat{Var} \left( \hat{\eta }\right) =15.009E+7 \end{array} \right] </math>
	\|-
	\| \hat{Cov}(\hat{\beta },\hat{\eta })=-2,664.40 ~~\|\| \|\|~~ \hat{Var} \left( \hat{\eta }\right) =15.009E+7 \end{array} \right] </math>
	The two-sided 95\ bounds on the parameters can be determined from the ‘‘‘QCP‘‘‘, in the ‘‘‘Parameter Bounds‘‘‘ tab.		The two-sided 95\ bounds on the parameters can be determined from the ‘‘‘QCP‘‘‘, in the ‘‘‘Parameter Bounds‘‘‘ tab.

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	FIGURE HERE		FIGURE HERE

	</math>		</math>



	==== Example 19====		==== Example 19====

Pengying niu: /* SUBSUBSECTION */

2011-02-28T19:01:03Z

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	Published Results for Example 18\ Weibull parameters (two-parameter Weibull, MLE):		Published Results for Example 18\ Weibull parameters (two-parameter Weibull, MLE):

	~~<math>~~		<math> \hat{\beta }=1.0584 </math>
	{\|		<math> \hat{\eta }=26,297 </math>
	\|-
	\| <math> \hat{\beta }=1.0584 </math>
	\|-
	\| <math> \hat{\eta }=26,297 </math>
	\|}
	~~</math>~~
	Published 95\\ FM confidence limits on the parameters:		Published 95\\ FM confidence limits on the parameters:

	~~<math>~~		<math> \hat{\beta }=\left\{ 0.64408,\text{ }1.7394\right\} </math>
	{\|		<math> \hat{\eta }=\left\{ 10,552,\text{ }65,535\right\} </math>
	\|-
	\| <math> \hat{\beta }=\left\{ 0.64408,\text{ }1.7394\right\} </math>
	\|-
	\| <math> \hat{\eta }=\left\{ 10,552,\text{ }65,535\right\} </math>
	\|}
	~~</math>~~
	Published variance/covariance matrix:		Published variance/covariance matrix:

	<math> \left[ \begin{array}{ccc} \hat{Var}\left( \hat{\beta }\right) =0.071958 ~~\|\| \|\|~~ \hat{Cov}( \hat{\beta },\hat{\eta })=-2,664.5		<math> \left[ \begin{array}{ccc} \hat{Var}\left( \hat{\beta }\right) =0.071958 & \hat{Cov}( \hat{\beta },\hat{\eta })=-2,664.5 \\
	\|-		\hat{Cov}(\hat{\beta },\hat{\eta })=-2,664.5 & \hat{Var} \left( \hat{\eta }\right) =15.010E+7 \end{array} \right] </math>
	~~\| \|\| \|\|~~		Note that Nelson expresses the results as multiples of <math> 1000 </math> (or <math> \hat{ \eta }=26.297, </math> etc.). The published results were adjusted by this factor to correlate with Weibull++ results.
	\|-
	\| \hat{Cov}(\hat{\beta },\hat{\eta })=-2,664.5 ~~\|\| \|\|~~ \hat{Var} \left( \hat{\eta }\right) =15.010E+7 \end{array} \right] </math>
	Note that Nelson expresses the results as multiples of <math> 1000 </math> (or <math> \hat{ \eta }=26.297, </math> etc.). The published results were adjusted by this factor to correlate with Weibull++ results.

	====SUBSUBSECTION====		====SUBSUBSECTION====