Gamma Distribution Example
Jump to navigation
Jump to search
[math]\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]
This example appears in the Life Data Analysis Reference book.
24 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]\begin{align} & \hat{\mu }= 7.72E-02 \\ & \hat{k}= 50.4908 \end{align}\,\![/math]
Using rank regression on [math]X,\,\![/math] the estimated parameters are:
- [math]\begin{align} & \hat{\mu }= 0.2915 \\ & \hat{k}= 41.1726 \end{align}\,\![/math]
Using rank regression on [math]Y,\,\![/math] the estimated parameters are:
- [math]\begin{align} & \hat{\mu }= 0.2915 \\ & \hat{k}= 41.1726 \end{align}\,\![/math]