Gamma Distribution Example: Difference between revisions

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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:  
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  & \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:  

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This example appears in the Life Data Analysis Reference book.

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

[math]\displaystyle{ \begin{matrix} \text{61} & \text{50} & \text{67} & \text{49} & \text{53} & \text{62} \\ \text{53} & \text{61} & \text{43} & \text{65} & \text{53} & \text{56} \\ \text{62} & \text{56} & \text{58} & \text{55} & \text{58} & \text{48} \\ \text{66} & \text{44} & \text{48} & \text{58} & \text{43} & \text{40} \\ \end{matrix} }[/math]

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

[math]\displaystyle{ \begin{align} & \hat{\mu }= 7.72E-02 \\ & \hat{k}= 50.4908 \end{align} }[/math]

Using rank regression on [math]\displaystyle{ X, }[/math] the estimated parameters are:

[math]\displaystyle{ \begin{align} & \hat{\mu }= 0.2915 \\ & \hat{k}= 41.1726 \end{align} }[/math]

Using rank regression on [math]\displaystyle{ Y, }[/math] the estimated parameters are:

[math]\displaystyle{ \begin{align} & \hat{\mu }= 0.2915 \\ & \hat{k}= 41.1726 \end{align} }[/math]