Template:Gll lognormal: Difference between revisions
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(Created page with '====GLL Lognormal==== <br> The GLL-lognormal model can be derived by setting <math>\breve{T}=L(\underline{X})</math> in Eqn. (GLL1), yielding the following GLL-lognormal <math…') |
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<math>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> | |||
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The total number of unknowns to solve for in this model is <math>n+2</math> (i.e. <math>{{\sigma }_{{{T}'}}},{{a}_{0}},{{a}_{1}},...{{a}_{n}}).</math> | The total number of unknowns to solve for in this model is <math>n+2</math> (i.e. <math>{{\sigma }_{{{T}'}}},{{a}_{0}},{{a}_{1}},...{{a}_{n}}).</math> | ||
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Revision as of 17:59, 14 February 2012
GLL Lognormal
The GLL-lognormal model can be derived by setting [math]\displaystyle{ \breve{T}=L(\underline{X}) }[/math]
in Eqn. (GLL1), 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]