Template:Gll lognormal

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

$$f(t,\underline{X})=\frac{1}{t\text{ }{{\sigma }_}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{{T}'-{{\alpha }_{0}}-\underset{j=1}{\overset{n}{\mathop{\sum }}}\,{{\alpha }_{j}}{{X}_{j}}}{{{\sigma }_}} \right)}^{2}}}}$$

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