Template:Example: 2P Weibull Distribution RRX - Revision history

Richard House: Redirected page to The Weibull Distribution#RRX Example

2012-08-21T04:19:24Z

Redirected page to The Weibull Distribution#RRX Example

← Older revision		Revision as of 04:19, 21 August 2012
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	~~'''2P Weibull Distribution RRX Example'''~~		#REDIRECT [[The_Weibull_Distribution#RRX_Example]]

	~~Repeat~~ [[~~Weibull Example 1 Data\|Example 1~~]] ~~using rank regression on X.~~

	~~'''Solution'''~~

	~~The Table constructed in [[Weibull Example 3 Data\|Example 3]], can also be applied to this example.~~

	~~Using the values from this table we get:~~

	::<math> \hat{b} ={\frac{\sum\limits_{i=1}^{6}(\ln T_{i})y_{i}-\frac{ \sum\limits_{i=1}^{6}\ln T_{i}\sum\limits_{i=1}^{6}y_{i}}{6}}{ \sum\limits_{i=1}^{6}y_{i}^{2}-\frac{\left( \sum\limits_{i=1}^{6}y_{i}\right) ^{2}}{6}}}
	~~</math>~~

	~~::<math>\hat{b} =\frac{-8.0699-(23.9068)(-3.0070)/6}{7.1502-(-3.0070)^{2}/6} </math>~~

	~~or:~~

	~~::<math> \hat{b}=0.6931 </math>~~

	~~and:~~

	~~::<math> \hat{a}=\overline{x}-\hat{b}\overline{y}=\frac{\sum\limits_{i=1}^{6}\ln T_{i} }{6}-\hat{b}\frac{\sum\limits_{i=1}^{6}y_{i}}{6} </math>~~

	~~or:~~

	~~::<math> \hat{a}=\frac{23.9068}{6}-(0.6931)\frac{(-3.0070)}{6}=4.3318 </math>~~

	~~Therefore:~~

	~~::<math> \hat{\beta }=\frac{1}{\hat{b}}=\frac{1}{0.6931}=1.4428 </math>~~

	~~and:~~

	~~::<math> \hat{\eta }=e^{\frac{\hat{a}}{\hat{b}}\cdot \frac{1}{\hat{ \beta }}}=e^{\frac{4.3318}{0.6931}\cdot \frac{1}{1.4428}}=76.0811\text{ hr} </math>~~

	~~The correlation coefficient is:~~

	~~::<math> \hat{\rho }=0.9956 </math>~~

	The results and the associated graph using Weibull++ are given next. Note that the slight variation in the results is due to the number of significant figures used in the estimation of the median ranks. Weibull++ by default uses double precision accuracy when computing the median ranks.

	~~[[Image:Weibull Distribution Example 4 RRX Plot.png\|center\|450px\| ]]~~

	~~<br>~~

Richard House at 05:38, 6 August 2012

2012-08-06T05:38:19Z

← Older revision		Revision as of 05:38, 6 August 2012
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	The results and the associated graph using Weibull++ are given next. Note that the slight variation in the results is due to the number of significant figures used in the estimation of the median ranks. Weibull++ by default uses double precision accuracy when computing the median ranks.		The results and the associated graph using Weibull++ are given next. Note that the slight variation in the results is due to the number of significant figures used in the estimation of the median ranks. Weibull++ by default uses double precision accuracy when computing the median ranks.

	[[Image:Weibull Distribution Example 4 RRX Plot.png~~\|thumb~~\|center\|450px\| ]]		[[Image:Weibull Distribution Example 4 RRX Plot.png\|center\|450px\| ]]

	<br>		<br>

Richard House at 05:07, 6 August 2012

2012-08-06T05:07:01Z

← Older revision		Revision as of 05:07, 6 August 2012
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	The results and the associated graph using Weibull++ are given next. Note that the slight variation in the results is due to the number of significant figures used in the estimation of the median ranks. Weibull++ by default uses double precision accuracy when computing the median ranks.		The results and the associated graph using Weibull++ are given next. Note that the slight variation in the results is due to the number of significant figures used in the estimation of the median ranks. Weibull++ by default uses double precision accuracy when computing the median ranks.

	[[Image:Weibull Distribution Example 4 RRX Plot.png\|thumb\|center\|~~250px~~\| ]]		[[Image:Weibull Distribution Example 4 RRX Plot.png\|thumb\|center\|450px\| ]]

	<br>		<br>

Nicolette Young at 18:14, 25 April 2012

2012-04-25T18:14:22Z

← Older revision		Revision as of 18:14, 25 April 2012
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	The results and the associated graph using Weibull++ are given next. Note that the slight variation in the results is due to the number of significant figures used in the estimation of the median ranks. Weibull++ by default uses double precision accuracy when computing the median ranks.		The results and the associated graph using Weibull++ are given next. Note that the slight variation in the results is due to the number of significant figures used in the estimation of the median ranks. Weibull++ by default uses double precision accuracy when computing the median ranks.

	[[Image:Weibull Distribution Example 4 RRX Plot.png\|thumb\|center\|~~400px~~\| ]]		[[Image:Weibull Distribution Example 4 RRX Plot.png\|thumb\|center\|250px\| ]]

	<br>		<br>

Harry Guo at 22:57, 1 March 2012

2012-03-01T22:57:52Z

← Older revision		Revision as of 22:57, 1 March 2012
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	The results and the associated graph using Weibull++ are given next. Note that the slight variation in the results is due to the number of significant figures used in the estimation of the median ranks. Weibull++ by default uses double precision accuracy when computing the median ranks.		The results and the associated graph using Weibull++ are given next. Note that the slight variation in the results is due to the number of significant figures used in the estimation of the median ranks. Weibull++ by default uses double precision accuracy when computing the median ranks.

	[[Image:~~onevariableplot~~.png\|thumb\|center\|400px\| ]]		[[Image:Weibull Distribution Example 4 RRX Plot.png\|thumb\|center\|400px\| ]]

	<br>		<br>

Harry Guo at 22:38, 9 February 2012

2012-02-09T22:38:01Z

← Older revision		Revision as of 22:38, 9 February 2012
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	'''2P Weibull Distribution RRX Example'''		'''2P Weibull Distribution RRX Example'''

	Repeat Example 1 using rank regression on X.		Repeat [[Weibull Example 1 Data\|Example 1]] using rank regression on X.

	'''Solution'''		'''Solution'''

	~~Solution to Example 4~~ Table ~~8.1,~~ constructed in Example 3, can also be applied to this example.		The Table constructed in [[Weibull Example 3 Data\|Example 3]], can also be applied to this example.

	Using the values from this table we get:		Using the values from this table we get:

Harry Guo at 22:35, 9 February 2012

2012-02-09T22:35:55Z

← Older revision		Revision as of 22:35, 9 February 2012
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	::<math>\hat{b} =\frac{-8.0699-(23.9068)(-3.0070)/6}{7.1502-(-3.0070)^{2}/6} </math>		::<math>\hat{b} =\frac{-8.0699-(23.9068)(-3.0070)/6}{7.1502-(-3.0070)^{2}/6} </math>

	:or:		or:

	::<math> \hat{b}=0.6931 </math>		::<math> \hat{b}=0.6931 </math>

	:and:		and:

	::<math> \hat{a}=\overline{x}-\hat{b}\overline{y}=\frac{\sum\limits_{i=1}^{6}\ln T_{i} }{6}-\hat{b}\frac{\sum\limits_{i=1}^{6}y_{i}}{6} </math>		::<math> \hat{a}=\overline{x}-\hat{b}\overline{y}=\frac{\sum\limits_{i=1}^{6}\ln T_{i} }{6}-\hat{b}\frac{\sum\limits_{i=1}^{6}y_{i}}{6} </math>

	:or:		or:

	::<math> \hat{a}=\frac{23.9068}{6}-(0.6931)\frac{(-3.0070)}{6}=4.3318 </math>		::<math> \hat{a}=\frac{23.9068}{6}-(0.6931)\frac{(-3.0070)}{6}=4.3318 </math>

	Therefore~~, from Eqn. (EQNREF bwx )~~:		Therefore:

	::<math> \hat{\beta }=\frac{1}{\hat{b}}=\frac{1}{0.6931}=1.4428 </math>		::<math> \hat{\beta }=\frac{1}{\hat{b}}=\frac{1}{0.6931}=1.4428 </math>

	:~~and from Eqn. (EQNREF awx )~~		and:

	::<math> \hat{\eta }=e^{\frac{\hat{a}}{\hat{b}}\cdot \frac{1}{\hat{ \beta }}}=e^{\frac{4.3318}{0.6931}\cdot \frac{1}{1.4428}}=76.0811\text{ hr} </math>		::<math> \hat{\eta }=e^{\frac{\hat{a}}{\hat{b}}\cdot \frac{1}{\hat{ \beta }}}=e^{\frac{4.3318}{0.6931}\cdot \frac{1}{1.4428}}=76.0811\text{ hr} </math>

	The correlation coefficient is ~~found using Eqn. (EQNREF RHOw )~~:		The correlation coefficient is:

	::<math> \hat{\rho }=0.9956 </math>		::<math> \hat{\rho }=0.9956 </math>

Harry Guo at 19:12, 9 February 2012

2012-02-09T19:12:25Z

← Older revision		Revision as of 19:12, 9 February 2012
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	'''2P Weibull Distribution RRX Example'''		'''2P Weibull Distribution RRX Example'''

	Repeat Example 1 using rank regression on X.		Repeat Example 1 using rank regression on X.

Harry Guo at 19:12, 9 February 2012

2012-02-09T19:12:15Z

← Older revision		Revision as of 19:12, 9 February 2012
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	~~==== Example 4:~~ 2P Weibull Distribution RRX Example ~~====~~		'''2P Weibull Distribution RRX Example'''
	Repeat Example 1 using rank regression on X.		Repeat Example 1 using rank regression on X.

Harry Guo: Created page with '==== Example 4: 2P Weibull Distribution RRX Example ==== Repeat Example 1 using rank regression on X. '''Solution''' Solution to Example 4 Table 8.1, constructed in Example 3, …'

2012-02-09T17:42:41Z

Created page with '==== Example 4: 2P Weibull Distribution RRX Example ==== Repeat Example 1 using rank regression on X. '''Solution''' Solution to Example 4 Table 8.1, constructed in Example 3, …'

New page

==== Example 4: 2P Weibull Distribution RRX Example ====
Repeat Example 1 using rank regression on X.

'''Solution'''

Solution to Example 4 Table 8.1, constructed in Example 3, can also be applied to this example.

Using the values from this table we get:

::<math> \hat{b} ={\frac{\sum\limits_{i=1}^{6}(\ln T_{i})y_{i}-\frac{ \sum\limits_{i=1}^{6}\ln T_{i}\sum\limits_{i=1}^{6}y_{i}}{6}}{ \sum\limits_{i=1}^{6}y_{i}^{2}-\frac{\left( \sum\limits_{i=1}^{6}y_{i}\right) ^{2}}{6}}}
</math>

::<math>\hat{b} =\frac{-8.0699-(23.9068)(-3.0070)/6}{7.1502-(-3.0070)^{2}/6} </math>

:or:

::<math> \hat{b}=0.6931 </math>

:and:

::<math> \hat{a}=\overline{x}-\hat{b}\overline{y}=\frac{\sum\limits_{i=1}^{6}\ln T_{i} }{6}-\hat{b}\frac{\sum\limits_{i=1}^{6}y_{i}}{6} </math>

:or:

::<math> \hat{a}=\frac{23.9068}{6}-(0.6931)\frac{(-3.0070)}{6}=4.3318 </math>

Therefore, from Eqn. (EQNREF bwx ):

::<math> \hat{\beta }=\frac{1}{\hat{b}}=\frac{1}{0.6931}=1.4428 </math>

:and from Eqn. (EQNREF awx )

::<math> \hat{\eta }=e^{\frac{\hat{a}}{\hat{b}}\cdot \frac{1}{\hat{ \beta }}}=e^{\frac{4.3318}{0.6931}\cdot \frac{1}{1.4428}}=76.0811\text{ hr} </math>

The correlation coefficient is found using Eqn. (EQNREF RHOw ):

::<math> \hat{\rho }=0.9956 </math>

The results and the associated graph using Weibull++ are given next. Note that the slight variation in the results is due to the number of significant figures used in the estimation of the median ranks. Weibull++ by default uses double precision accuracy when computing the median ranks.

[[Image:onevariableplot.png|thumb|center|400px| ]]

<br>