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| '''A Gamma Distribution Example'''
| | #REDIRECT [[Example:_Gamma_Distribution]] |
| [[Example: Gamma Distribution]] | |
| Twenty four units were reliability tested and the following life test data were obtained:
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| <center><math>\begin{matrix}
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| \text{61} & \text{50} & \text{67} & \text{49} & \text{53} & \text{62} \\
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| \text{53} & \text{61} & \text{43} & \text{65} & \text{53} & \text{56} \\
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| \text{62} & \text{56} & \text{58} & \text{55} & \text{58} & \text{48} \\
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| \text{66} & \text{44} & \text{48} & \text{58} & \text{43} & \text{40} \\
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| \end{matrix}</math></center>
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| Fitting the gamma distribution to this data, using maximum likelihood as the analysis method, gives the following parameters:
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| ::<math>\begin{align}
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| & \hat{\mu }= 7.72E-02 \\
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| & \hat{k}= 50.4908
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| \end{align}</math>
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| Using rank regression on <math>X,</math> the estimated parameters are:
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| ::<math>\begin{align}
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| & \hat{\mu }= 0.2915 \\
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| & \hat{k}= 41.1726
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| \end{align}</math>
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| Using rank regression on <math>Y,</math> the estimated parameters are:
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| ::<math>\begin{align}
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| & \hat{\mu }= 0.2915 \\
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| & \hat{k}= 41.1726
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| \end{align}</math>
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