Gamma Distribution Example

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This example appears in the Life Data Analysis Reference book.

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

\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}\,\!

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

\begin{align}
  & \hat{\mu }=  7.72E-02 \\ 
 & \hat{k}=  50.4908  
\end{align}\,\!

Using rank regression on X,\,\! the estimated parameters are:

\begin{align}
  & \hat{\mu }=  0.2915 \\ 
 & \hat{k}=  41.1726  
\end{align}\,\!

Using rank regression on Y,\,\! the estimated parameters are:

\begin{align}
  & \hat{\mu }=  0.2915 \\ 
 & \hat{k}=  41.1726  
\end{align}\,\!
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