ALTA ALTA Standard Folio Data TNT-Lognormal: Difference between revisions

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The T-NT lognormal model <math>pdf</math> can be obtained first by setting <math>\overline{T}=L(V)</math>
in Eqn. (Temp-Volt).
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Therefore:
 
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<math>\breve{T}=L(V)=\frac{C}{{{U}^{n}}}{{e}^{\tfrac{B}{V}}}</math>
 
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or:
 
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<math>{{e}^{{{\overline{T}}^{\prime }}}}=\frac{C}{{{U}^{n}}}{{e}^{\tfrac{B}{V}}}</math>
 
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Thus:
 
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<math>{{\overline{T}}^{\prime }}=\ln (C)-n\ln (U)+\frac{B}{V}</math>
 
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Substituting Eqn.(TV-logn-mean)into Eqn. (TV-logn-pdf) yields the T-NT lognormal model  <math>pdf</math> or:
 
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<math>f(T,U,V)=\frac{1}{T\text{ }{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{{T}'-\ln (C)+n\ln (U)-\tfrac{B}{V}}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}}</math>
 
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Latest revision as of 20:00, 8 July 2015

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