Gamma Distribution Example: Difference between revisions
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<noinclude>{{Banner Weibull Examples}} | <noinclude>{{Banner Weibull Examples}} | ||
''This example appears in the [ | ''This example appears in the [https://help.reliasoft.com/reference/life_data_analysis Life data analysis reference]''.</noinclude> | ||
24 units were reliability tested, and the following life test data were obtained: | 24 units were reliability tested, and the following life test data were obtained: | ||
{| border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5" | |||
|- align="center" | |||
|61 ||50||67||49||53||62 | |||
|- align="center" | |||
|53||61||43||65||53||56 | |||
|- align="center" | |||
|62||56||58||55||58||48 | |||
|- align="center" | |||
|66||44||48||58||43||40 | |||
|} | |||
Fitting the gamma distribution to this data, using maximum likelihood as the analysis method, gives the following parameters: | Fitting the gamma distribution to this data, using maximum likelihood as the analysis method, gives the following parameters: | ||
| Line 16: | Line 20: | ||
& \hat{\mu }= 7.72E-02 \\ | & \hat{\mu }= 7.72E-02 \\ | ||
& \hat{k}= 50.4908 | & \hat{k}= 50.4908 | ||
\end{align}</math> | \end{align}\,\!</math> | ||
Using rank regression on | Using rank regression on <math>X,\,\!</math> the estimated parameters are: | ||
::<math>\begin{align} | ::<math>\begin{align} | ||
& \hat{\mu }= 0.2915 \\ | & \hat{\mu }= 0.2915 \\ | ||
& \hat{k}= 41.1726 | & \hat{k}= 41.1726 | ||
\end{align}</math> | \end{align}\,\!</math> | ||
Using rank regression on | Using rank regression on <math>Y,\,\!</math> the estimated parameters are: | ||
::<math>\begin{align} | ::<math>\begin{align} | ||
& \hat{\mu }= 0.2915 \\ | & \hat{\mu }= 0.2915 \\ | ||
& \hat{k}= 41.1726 | & \hat{k}= 41.1726 | ||
\end{align}</math> | \end{align}\,\!</math> | ||
Latest revision as of 21:38, 18 September 2023
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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]