Template:Three-parameter weibull distribution: Difference between revisions
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(Created page with '=== The Three-Parameter Weibull Distribution === The three-parameter Weibull ''pdf'' is given by: ::<math> f(T)={ \frac{\beta }{\eta }}\left( {\frac{T-\gamma }{\eta }}\right) …') |
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The three-parameter Weibull ''pdf'' is given by: | The three-parameter Weibull ''pdf'' is given by: | ||
::<math> f( | ::<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( | ::<math> f(t)\geq 0,\text{ }T\geq 0\text{ or }\gamma, </math> | ||
::<math>\beta>0\ \,\!</math>, | ::<math>\beta>0\ \,\!</math>, | ||
Revision as of 19:11, 3 February 2012
The Three-Parameter Weibull Distribution
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).