Gamma Distribution Example: Difference between revisions

From ReliaWiki
Jump to navigation Jump to search
No edit summary
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}
Line 25: Line 25:
\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}

Revision as of 03:09, 28 August 2012

Weibull Examples Banner.png


New format available! This reference is now available in a new format that offers faster page load, improved display for calculations and images and more targeted search.

As of January 2024, this Reliawiki page will not continue to be updated. Please update all links and bookmarks to the latest references at Weibull examples and Weibull reference examples.




This example appears in the Life Data Analysis Reference book.

24 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]