Gamma Distribution Example: Difference between revisions

From ReliaWiki
Jump to navigation Jump to search
No edit summary
No edit summary
 
(4 intermediate revisions by 2 users not shown)
Line 1: Line 1:
<noinclude>{{Banner Weibull Examples}}
<noinclude>{{Banner Weibull Examples}}
''This example appears in the [[The_Gamma_Distribution#General_Example|Life Data Analysis Reference book]]''.</noinclude>
''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:


<center><math>\begin{matrix}
{| border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
  \text{61} & \text{50} & \text{67} & \text{49} & \text{53} & \text{62}  \\
|- align="center"
  \text{53} & \text{61} & \text{43} & \text{65} & \text{53} & \text{56}  \\
|61 ||50||67||49||53||62
  \text{62} & \text{56} & \text{58} & \text{55} & \text{58} & \text{48}  \\
|- align="center"
  \text{66} & \text{44} & \text{48} & \text{58} & \text{43} & \text{40}  \\
|53||61||43||65||53||56
\end{matrix}</math></center>
|- 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 <math>X,\,\!</math> the estimated parameters are:  
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 <math>Y,\,\!</math> the estimated parameters are:  
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

Weibull Examples Banner.png


New format available! This reference is now available in a new format that offers faster page load, improved display for calculations and images and more targeted search.

As of January 2024, this Reliawiki page will not continue to be updated. Please update all links and bookmarks to the latest references at Weibull examples and Weibull reference examples.



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]
Retrieved from "https://www.reliawiki.com/index.php?title=Gamma_Distribution_Example&oldid=66161"