Template:Gll weibull

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

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

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