Template:Three-parameter weibull distribution: Difference between revisions
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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> | ||
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::<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)