Template:Example: Gamma Distribution Example: Difference between revisions
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[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]
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::<math>\begin{align} | ::<math>\begin{align} | ||
& \hat{\mu }= | & \hat{\mu }= 0.2915 \\ | ||
& \hat{k}= | & \hat{k}= 41.1726 | ||
\end{align}</math> | \end{align}</math> | ||
| Line 28: | Line 28: | ||
::<math>\begin{align} | ::<math>\begin{align} | ||
& \hat{\mu }= | & \hat{\mu }= 0.2915 \\ | ||
& \hat{k}= | & \hat{k}= 41.1726 | ||
\end{align}</math> | \end{align}</math> | ||
Revision as of 22:31, 14 February 2012
A Gamma Distribution Example
Twenty four units were reliability tested and the following life test data were obtained:
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]