Template:Three-parameter weibull distribution: Difference between revisions

From ReliaWiki
Jump to navigation Jump to search
No edit summary
No edit summary
Line 1: Line 1:
The 3-parameter Weibull ''pdf'' is given by:  
The 3-parameter Weibull ''pdf'' is given by:  


::<math> f(t)={ \frac{\beta }{\eta }}\left( {\frac{t-\gamma }{\eta }}\right) ^{\beta -1}e^{-\left( {\frac{t-\gamma }{\eta }}\right) ^{\beta }} </math>  
::<math> f(t)={ \frac{\beta }{\eta }}\left( {\frac{t-\gamma }{\eta }}\right) ^{\beta -1}e^{-\left( {\frac{t-\gamma }{\eta }}\right) ^{\beta }} \,\!</math>  


where:
where:


::<math> f(t)\geq 0,\text{ }t\geq 0\text{ or }\gamma </math>
::<math> f(t)\geq 0,\text{ }t\geq 0\text{ or }\gamma \,\!</math>


::<math>\beta>0\ \,\!</math>
::<math>\beta>0\ \,\!</math>
Line 11: Line 11:
::<math> \eta > 0 \,\!</math>
::<math> \eta > 0 \,\!</math>


::<math> -\infty < \gamma < +\infty </math>
::<math> -\infty < \gamma < +\infty \,\!</math>


and:  
and:  

Revision as of 18:35, 25 September 2012

The 3-parameter Weibull pdf is given by:

[math]\displaystyle{ f(t)={ \frac{\beta }{\eta }}\left( {\frac{t-\gamma }{\eta }}\right) ^{\beta -1}e^{-\left( {\frac{t-\gamma }{\eta }}\right) ^{\beta }} \,\! }[/math]

where:

[math]\displaystyle{ f(t)\geq 0,\text{ }t\geq 0\text{ or }\gamma \,\! }[/math]
[math]\displaystyle{ \beta\gt 0\ \,\! }[/math]
[math]\displaystyle{ \eta \gt 0 \,\! }[/math]
[math]\displaystyle{ -\infty \lt \gamma \lt +\infty \,\! }[/math]

and:

[math]\displaystyle{ \eta= \,\! }[/math] scale parameter, or characteristic life
[math]\displaystyle{ \beta= \,\! }[/math] shape parameter (or slope)
[math]\displaystyle{ \gamma= \,\! }[/math] location parameter (or failure free life)