Gamma Distribution Example - Revision history

Lisa Hacker at 21:38, 18 September 2023

2023-09-18T21:38:19Z

← Older revision		Revision as of 21:38, 18 September 2023
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	<noinclude>{{Banner Weibull Examples}}		<noinclude>{{Banner Weibull Examples}}
	''This example appears in the [~~[The_Gamma_Distribution#General_Example\|~~Life ~~Data Analysis Reference book]~~]''.</noinclude>		''This example appears in the [https://help.reliasoft.com/reference/life_data_analysis Life data analysis reference]''.</noinclude>

	24 units were reliability tested, and the following life test data were obtained:		24 units were reliability tested, and the following life test data were obtained:

Lisa Hacker at 01:02, 9 March 2023

2023-03-09T01:02:08Z

← Older revision		Revision as of 01:02, 9 March 2023
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	\|62\|\|56\|\|58\|\|55\|\|58\|\|48		\|62\|\|56\|\|58\|\|55\|\|58\|\|48
	\|- align="center"		\|- align="center"
	\|66\|44\|\|48\|\|58\|\|43\|\|40		\|66\|\|44\|\|48\|\|58\|\|43\|\|40
	\|}		\|}

Lisa Hacker at 01:01, 9 March 2023

2023-03-09T01:01:03Z

← Older revision		Revision as of 01:01, 9 March 2023
Line 4:		Line 4:
	24 units were reliability tested, and the following life test data were obtained:		24 units were reliability tested, and the following life test data were obtained:

	<center~~><math>\begin{matrix}~~		{\| border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
	~~\text{~~61~~} & \text{~~50~~} & \text{~~67~~} & \text{~~49~~} & \text{~~53~~} & \text{~~62~~} \\~~		\|- align="center"
	~~\text{~~53~~} & \text{~~61~~} & \text{~~43~~} & \text{~~65~~} & \text{~~53~~} & \text{~~56~~} \\~~		\|61 \|\|50\|\|67\|\|49\|\|53\|\|62
	~~\text{~~62~~} & \text{~~56~~} & \text{~~58~~} & \text{~~55~~} & \text{~~58~~} & \text{~~48~~} \\~~		\|- align="center"
	~~\text{~~66~~} & \text{~~44~~} & \text{~~48~~} & \text{~~58~~} & \text{~~43~~} & \text{~~40~~} \\~~		\|53\|\|61\|\|43\|\|65\|\|53\|\|56
	~~\end{matrix~~}~~\,\!</math></center>~~		\|- align="center"
			\|62\|\|56\|\|58\|\|55\|\|58\|\|48
			\|- align="center"
			\|66\|44\|\|48\|\|58\|\|43\|\|40
			\|}

	Fitting the gamma distribution to this data, using maximum likelihood as the analysis method, gives the following parameters:		Fitting the gamma distribution to this data, using maximum likelihood as the analysis method, gives the following parameters:

Richard House at 16:21, 26 September 2012

2012-09-26T16:21:23Z

← Older revision		Revision as of 16:21, 26 September 2012
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	\text{62} & \text{56} & \text{58} & \text{55} & \text{58} & \text{48} \\		\text{62} & \text{56} & \text{58} & \text{55} & \text{58} & \text{48} \\
	\text{66} & \text{44} & \text{48} & \text{58} & \text{43} & \text{40} \\		\text{66} & \text{44} & \text{48} & \text{58} & \text{43} & \text{40} \\
	\end{matrix}</math>~~\,\!~~</center>		\end{matrix}\,\!</math></center>

	Fitting the gamma distribution to this data, using maximum likelihood as the analysis method, gives the following parameters:		Fitting the gamma distribution to this data, using maximum likelihood as the analysis method, gives the following parameters:

Richard House at 16:14, 26 September 2012

2012-09-26T16:14:37Z

← Older revision		Revision as of 16:14, 26 September 2012
Line 9:		Line 9:
	\text{62} & \text{56} & \text{58} & \text{55} & \text{58} & \text{48} \\		\text{62} & \text{56} & \text{58} & \text{55} & \text{58} & \text{48} \\
	\text{66} & \text{44} & \text{48} & \text{58} & \text{43} & \text{40} \\		\text{66} & \text{44} & \text{48} & \text{58} & \text{43} & \text{40} \\
	\end{matrix}</math></center>		\end{matrix}</math>\,\!</center>

	Fitting the gamma distribution to this data, using maximum likelihood as the analysis method, gives the following parameters:		Fitting the gamma distribution to this data, using maximum likelihood as the analysis method, gives the following parameters:
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	& \hat{\mu }= 7.72E-02 \\		& \hat{\mu }= 7.72E-02 \\
	& \hat{k}= 50.4908		& \hat{k}= 50.4908
	\end{align}</math>		\end{align}\,\!</math>

	Using rank regression on <math>X,\,\!</math> the estimated parameters are:		Using rank regression on <math>X,\,\!</math> the estimated parameters are:

	::<math>\begin{align}		::<math>\begin{align}
	& \hat{\mu }= 0.2915 \\		& \hat{\mu }= 0.2915 \\
	& \hat{k}= 41.1726		& \hat{k}= 41.1726
	\end{align}</math>		\end{align}\,\!</math>

	Using rank regression on <math>Y,\,\!</math> the estimated parameters are:		Using rank regression on <math>Y,\,\!</math> the estimated parameters are:

	::<math>\begin{align}		::<math>\begin{align}
	& \hat{\mu }= 0.2915 \\		& \hat{\mu }= 0.2915 \\
	& \hat{k}= 41.1726		& \hat{k}= 41.1726
	\end{align}</math>		\end{align}\,\!</math>

Richard House at 03:09, 28 August 2012

2012-08-28T03:09:52Z

← Older revision		Revision as of 03:09, 28 August 2012
Line 18:		Line 18:
	\end{align}</math>		\end{align}</math>

	Using rank regression on <math>X,</math> the estimated parameters are:		Using rank regression on <math>X,\,\!</math> the estimated parameters are:

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

	Using rank regression on <math>Y,</math> the estimated parameters are:		Using rank regression on <math>Y,\,\!</math> the estimated parameters are:

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

Chris Kahn: moved Example: Gamma Distribution to Gamma Distribution Example

2012-08-20T01:08:44Z

moved Example: Gamma Distribution to Gamma Distribution Example

← Older revision	Revision as of 01:08, 20 August 2012
(No difference)

Chris Kahn at 01:00, 20 August 2012

2012-08-20T01:00:34Z

← Older revision		Revision as of 01:00, 20 August 2012
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	''This example appears in the [[The_Gamma_Distribution#General_Example\|Life Data Analysis Reference book]]''.</noinclude>		''This example appears in the [[The_Gamma_Distribution#General_Example\|Life Data Analysis Reference book]]''.</noinclude>

	~~Twenty four~~ units were reliability tested and the following life test data were obtained:		24 units were reliability tested, and the following life test data were obtained:

	<center><math>\begin{matrix}		<center><math>\begin{matrix}

Richard House at 07:48, 7 August 2012

2012-08-07T07:48:32Z

← Older revision		Revision as of 07:48, 7 August 2012
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	<noinclude>{{Banner Weibull Examples}}		<noinclude>{{Banner Weibull Examples}}
	''This example appears in the [[The_Gamma_Distribution#General_Example\|Life Data Analysis Reference book]]''.</noinclude>		''This example appears in the [[The_Gamma_Distribution#General_Example\|Life Data Analysis Reference book]]''.</noinclude>


	Twenty four units were reliability tested and the following life test data were obtained:		Twenty four units were reliability tested and the following life test data were obtained:
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	\text{66} & \text{44} & \text{48} & \text{58} & \text{43} & \text{40} \\		\text{66} & \text{44} & \text{48} & \text{58} & \text{43} & \text{40} \\
	\end{matrix}</math></center>		\end{matrix}</math></center>


	Fitting the gamma distribution to this data, using maximum likelihood as the analysis method, gives the following parameters:		Fitting the gamma distribution to this data, using maximum likelihood as the analysis method, gives the following parameters:
Line 19:		Line 17:
	& \hat{k}= 50.4908		& \hat{k}= 50.4908
	\end{align}</math>		\end{align}</math>


	Using rank regression on <math>X,</math> the estimated parameters are:		Using rank regression on <math>X,</math> the estimated parameters are:
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	& \hat{k}= 41.1726		& \hat{k}= 41.1726
	\end{align}</math>		\end{align}</math>


	Using rank regression on <math>Y,</math> the estimated parameters are:		Using rank regression on <math>Y,</math> the estimated parameters are:

Kate Racaza: proofread

2012-07-23T09:27:02Z

proofread

← Older revision		Revision as of 09:27, 23 July 2012
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	{~~\| class="FCK__ShowTableBorders" border="0" cellspacing="0" cellpadding="0" align="center"; style="width:100%;"~~		<noinclude>{{Banner Weibull Examples}}
	\|-		''This example appears in the [[The_Gamma_Distribution#General_Example\|Life Data Analysis Reference book]]''.</noinclude>
	~~\| valign="middle" align="left" bgcolor=EEEDF7\|~~[[~~Image:Weibull-Examples-banner.png\|400px~~\|~~center~~]]
	\|}
	~~<br>~~Twenty four units were reliability tested and the following life test data were obtained:		Twenty four units were reliability tested and the following life test data were obtained:

	<center><math>\begin{matrix}		<center><math>\begin{matrix}
Line 11:		Line 11:
	\text{66} & \text{44} & \text{48} & \text{58} & \text{43} & \text{40} \\		\text{66} & \text{44} & \text{48} & \text{58} & \text{43} & \text{40} \\
	\end{matrix}</math></center>		\end{matrix}</math></center>


	Fitting the gamma distribution to this data, using maximum likelihood as the analysis method, gives the following parameters:		Fitting the gamma distribution to this data, using maximum likelihood as the analysis method, gives the following parameters:
Line 18:		Line 19:
	& \hat{k}= 50.4908		& \hat{k}= 50.4908
	\end{align}</math>		\end{align}</math>


	Using rank regression on <math>X,</math> the estimated parameters are:		Using rank regression on <math>X,</math> the estimated parameters are: