Template:Gll exponential

GLL Exponential

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

[math]\displaystyle{ 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}} }[/math]

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