Template:Gll lognormal

GLL Lognormal

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

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

The total number of unknowns to solve for in this model is [math]\displaystyle{ n+2 }[/math] (i.e. [math]\displaystyle{ {{\sigma }_{{{T}'}}},{{a}_{0}},{{a}_{1}},...{{a}_{n}}). }[/math]