Template: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).