Template:Example: Generalized Gamma Distribution Example - Revision history

Lisa Hacker: Redirected page to Example: Generalized Gamma Distribution Example

2012-08-15T03:58:23Z

Redirected page to Example: Generalized Gamma Distribution Example

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	[[~~Category~~: ~~For Deletion~~]]		#REDIRECT [[Example:_Generalized_Gamma_Distribution_Example]]

Kate Racaza: Replaced content with 'Category: For Deletion'

2012-07-23T09:17:45Z

Replaced content with 'Category: For Deletion'

← Older revision		Revision as of 09:17, 23 July 2012
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	~~'''A Generalized Gamma Distribution Example'''~~		[[Category: For Deletion]]

	~~The following data set represents revolutions-to-failure (in millions) for 23 ball bearings in a fatigue test~~ [[~~Appendix~~: ~~Weibull References\|[21]]].~~


	~~::<math>\begin{array}{*{35}{l}}~~
	\text{17}\text{.88} & \text{28}\text{.92} & \text{33} & \text{41}\text{.52} & \text{42}\text{.12} & \text{45}\text{.6} & \text{48}\text{.4} & \text{51}\text{.84} & \text{51}\text{.96} & \text{54}\text{.12} \\
	\text{55}\text{.56} & \text{67}\text{.8} & \text{68}\text{.64} & \text{68}\text{.64} & \text{68}\text{.88} & \text{84}\text{.12} & \text{93}\text{.12} & \text{98}\text{.64} & \text{105}\text{.12} & \text{105}\text{.84} \\
	~~\text{127}\text{.92} & \text{128}\text{.04} & \text{173}\text{.4} & {} & {} & {} & {} & {} & {} & {} \\~~
	~~\end{array}</math>~~


	~~When the generalized gamma distribution is fitted to this data using MLE, the following values for parameters are obtained:~~

	~~::<math>\begin{align}~~
	~~& \widehat{\mu }= & 4.23064 \\~~
	~~& \widehat{\sigma }= & 0.509982 \\~~
	~~& \widehat{\lambda }= & 0.307639~~
	~~\end{align}</math>~~

	Note that for this data, the generalized gamma offers a compromise between the Weibull <math>(\lambda =1),</math> and the lognormal <math>(\lambda =0)</math> distributions. The value of <math>\lambda </math> indicates that the lognormal distribution is better supported by the data. A better assessment, however, can be made by looking at the confidence bounds on <math>\lambda .</math> For ~~example, the 90% two-sided confidence bounds are:~~

	~~::<math>\begin{align}~~
	~~& {{\lambda }_{u}}= & -0.592087 \\~~
	~~& {{\lambda }_{u}}= & 1.20736~~
	~~\end{align}</math>~~

	~~It can be then concluded that both distributions (i.e. Weibull and lognormal) are well supported by the data, with the lognormal being the ,better supported of the two.~~
	~~In Weibull++ the generalized gamma probability is plotted on gamma probability paper, as shown next.~~

	~~[[Image:GGamma Example 1 Plot.png\|thumb\|center\|250px\|~~ ]]

	It is important to also note that as in the case of the mixed Weibull distribution, in the case of regression analysis, using a generalized gamma model, the choice of regression axis, i.e. <math>RRX</math> or <math>RRY,</math> is of no consequence since non-linear regression is utilized.

Kate Racaza: removed link to http://reliawiki.org/index.php/Example:_Generalized_Gamma_Distribution_Example

2012-07-10T11:19:29Z

removed link to http://reliawiki.org/index.php/Example:_Generalized_Gamma_Distribution_Example

← Older revision		Revision as of 11:19, 10 July 2012
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	'''A Generalized Gamma Distribution Example'''		'''A Generalized Gamma Distribution Example'''
	~~[[Example: Generalized Gamma Distribution Example]]~~
	The following data set represents revolutions-to-failure (in millions) for 23 ball bearings in a fatigue test [[Appendix: Weibull References\|[21]]].		The following data set represents revolutions-to-failure (in millions) for 23 ball bearings in a fatigue test [[Appendix: Weibull References\|[21]]].

Nicolette Young at 21:56, 25 April 2012

2012-04-25T21:56:50Z

← Older revision		Revision as of 21:56, 25 April 2012
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	In Weibull++ the generalized gamma probability is plotted on gamma probability paper, as shown next.		In Weibull++ the generalized gamma probability is plotted on gamma probability paper, as shown next.

	[[Image:GGamma Example 1 Plot.png\|thumb\|center\|~~500px~~\| ]]		[[Image:GGamma Example 1 Plot.png\|thumb\|center\|250px\| ]]

	It is important to also note that as in the case of the mixed Weibull distribution, in the case of regression analysis, using a generalized gamma model, the choice of regression axis, i.e. <math>RRX</math> or <math>RRY,</math> is of no consequence since non-linear regression is utilized.		It is important to also note that as in the case of the mixed Weibull distribution, in the case of regression analysis, using a generalized gamma model, the choice of regression axis, i.e. <math>RRX</math> or <math>RRY,</math> is of no consequence since non-linear regression is utilized.

Nicolette Young at 23:39, 21 March 2012

2012-03-21T23:39:13Z

← Older revision		Revision as of 23:39, 21 March 2012
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	'''A Generalized Gamma Distribution Example'''		'''A Generalized Gamma Distribution Example'''
			[[Example: Generalized Gamma Distribution Example]]
	The following data set represents revolutions-to-failure (in millions) for 23 ball bearings in a fatigue test [[Appendix: Weibull References\|[21]]].		The following data set represents revolutions-to-failure (in millions) for 23 ball bearings in a fatigue test [[Appendix: Weibull References\|[21]]].

Harry Guo at 17:30, 2 March 2012

2012-03-02T17:30:36Z

← Older revision		Revision as of 17:30, 2 March 2012
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	In Weibull++ the generalized gamma probability is plotted on gamma probability paper, as shown next.		In Weibull++ the generalized gamma probability is plotted on gamma probability paper, as shown next.

	[[Image:~~ldagamma10~~.~~2.gif~~\|thumb\|center\|500px\| ]]		[[Image:GGamma Example 1 Plot.png\|thumb\|center\|500px\| ]]

	It is important to also note that as in the case of the mixed Weibull distribution, in the case of regression analysis, using a generalized gamma model, the choice of regression axis, i.e. <math>RRX</math> or <math>RRY,</math> is of no consequence since non-linear regression is utilized.		It is important to also note that as in the case of the mixed Weibull distribution, in the case of regression analysis, using a generalized gamma model, the choice of regression axis, i.e. <math>RRX</math> or <math>RRY,</math> is of no consequence since non-linear regression is utilized.

Harry Guo at 21:56, 14 February 2012

2012-02-14T21:56:41Z

← Older revision		Revision as of 21:56, 14 February 2012
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	\text{127}\text{.92} & \text{128}\text{.04} & \text{173}\text{.4} & {} & {} & {} & {} & {} & {} & {} \\		\text{127}\text{.92} & \text{128}\text{.04} & \text{173}\text{.4} & {} & {} & {} & {} & {} & {} & {} \\
	\end{array}</math>		\end{array}</math>


	When the generalized gamma distribution is fitted to this data using MLE, the following values for parameters are obtained:		When the generalized gamma distribution is fitted to this data using MLE, the following values for parameters are obtained:

Harry Guo: /* A Generalized Gamma Distribution Example */

2012-02-14T18:44:16Z

A Generalized Gamma Distribution Example

← Older revision		Revision as of 18:44, 14 February 2012
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	~~====~~A Generalized Gamma Distribution Example~~====~~		'''A Generalized Gamma Distribution Example'''
	The following data set represents revolutions-to-failure (in millions) for 23 ball bearings in a fatigue test [21].
			The following data set represents revolutions-to-failure (in millions) for 23 ball bearings in a fatigue test [[Appendix: Weibull References\|[21]]].

Harry Guo: moved Template:Generalized gamma example to Template:Example: Generalized Gamma Distribution Example

2012-02-14T18:42:40Z

moved Template:Generalized gamma example to Template:Example: Generalized Gamma Distribution Example

← Older revision	Revision as of 18:42, 14 February 2012
(No difference)

Nicolette Young: Created page with '====A Generalized Gamma Distribution Example==== The following data set represents revolutions-to-failure (in millions) for 23 ball bearings in a fatigue test [21]. :: $\be…'$

2012-01-19T22:26:58Z

Created page with '====A Generalized Gamma Distribution Example==== The following data set represents revolutions-to-failure (in millions) for 23 ball bearings in a fatigue test [21]. ::<math>\be…'

New page

====A Generalized Gamma Distribution Example====
The following data set represents revolutions-to-failure (in millions) for 23 ball bearings in a fatigue test [21].

::<math>\begin{array}{*{35}{l}}
\text{17}\text{.88} & \text{28}\text{.92} & \text{33} & \text{41}\text{.52} & \text{42}\text{.12} & \text{45}\text{.6} & \text{48}\text{.4} & \text{51}\text{.84} & \text{51}\text{.96} & \text{54}\text{.12} \\
\text{55}\text{.56} & \text{67}\text{.8} & \text{68}\text{.64} & \text{68}\text{.64} & \text{68}\text{.88} & \text{84}\text{.12} & \text{93}\text{.12} & \text{98}\text{.64} & \text{105}\text{.12} & \text{105}\text{.84} \\
\text{127}\text{.92} & \text{128}\text{.04} & \text{173}\text{.4} & {} & {} & {} & {} & {} & {} & {} \\
\end{array}</math>

When the generalized gamma distribution is fitted to this data using MLE, the following values for parameters are obtained:

::<math>\begin{align}
& \widehat{\mu }= & 4.23064 \\
& \widehat{\sigma }= & 0.509982 \\
& \widehat{\lambda }= & 0.307639
\end{align}</math>

Note that for this data, the generalized gamma offers a compromise between the Weibull <math>(\lambda =1),</math> and the lognormal <math>(\lambda =0)</math> distributions. The value of <math>\lambda </math> indicates that the lognormal distribution is better supported by the data. A better assessment, however, can be made by looking at the confidence bounds on <math>\lambda .</math> For example, the 90% two-sided confidence bounds are:

::<math>\begin{align}
& {{\lambda }_{u}}= & -0.592087 \\
& {{\lambda }_{u}}= & 1.20736
\end{align}</math>

It can be then concluded that both distributions (i.e. Weibull and lognormal) are well supported by the data, with the lognormal being the ,better supported of the two.
In Weibull++ the generalized gamma probability is plotted on gamma probability paper, as shown next.

[[Image:ldagamma10.2.gif|thumb|center|500px| ]]

It is important to also note that as in the case of the mixed Weibull distribution, in the case of regression analysis, using a generalized gamma model, the choice of regression axis, i.e. <math>RRX</math> or <math>RRY,</math> is of no consequence since non-linear regression is utilized.