Template:Gll weibull

GLL Weibull

The GLL-Weibull model can be derived by setting [math]\displaystyle{ \eta =L(\underline{X}) }[/math] in Weibull [math]\displaystyle{ pdf }[/math], yielding the following GLL-Weibull [math]\displaystyle{ pdf }[/math] :

[math]\displaystyle{ f(t,\underline{X})=\beta \cdot {{t}^{\beta -1}}{{e}^{-\beta \left( {{\alpha }_{0}}+\underset{j=1}{\overset{n}{\mathop{\sum }}}\,{{\alpha }_{j}}{{X}_{j}} \right)}}{{e}^{-{{t}^{\beta }}{{e}^{-\beta \left( {{\alpha }_{0}}+\underset{j=1}{\overset{n}{\mathop{\sum }}}\,{{\alpha }_{j}}{{X}_{j}} \right)}}}} }[/math]

The total number of unknowns to solve for in this model is [math]\displaystyle{ n+2 }[/math] (i.e. [math]\displaystyle{ \beta ,{{a}_{0}},{{a}_{1}},...{{a}_{n}}). }[/math]