Template:Three-parameter weibull distribution: Difference between revisions

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=== The Three-Parameter Weibull Distribution ===
The three-parameter Weibull ''pdf'' is given by:  
The three-parameter Weibull ''pdf'' is given by:  



Revision as of 17:42, 8 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).