Template:Gll exponential

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

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

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