Template:Three-parameter weibull distribution: Difference between revisions
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::<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, | |||
::<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> | ||
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::<math> -\infty < \gamma < +\infty \,\!</math> | ::<math> -\infty < \gamma < +\infty \,\!</math> | ||
and, | |||
::<math> \eta= \,\!</math> scale parameter, or characteristic life | ::<math> \eta= \,\!</math> scale parameter, or characteristic life | ||
::<math> \beta= \,\!</math> shape parameter (or slope), | ::<math> \beta= \,\!</math> shape parameter (or slope), | ||
::<math> \gamma= \,\!</math> location parameter (or failure free life). | ::<math> \gamma= \,\!</math> location parameter (or failure free life). | ||
Revision as of 21:28, 9 February 2012
The three-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).