Gamma Distribution Example

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This example appears in the Life data analysis reference.

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

61 50 67 49 53 62
53 61 43 65 53 56
62 56 58 55 58 48
66 44 48 58 43 40

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]