Template:Example: Gamma Distribution Example

A Gamma Distribution Example
Twenty four 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}$$