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>  
The T-NT lognormal model <math>pdf</math> can be obtained first by setting <math>\overline{T}=L(V)</math>  
in Eqn. (Temp-Volt).  
in Eqn. (Temp-Volt).  
<br>
<br>
Therefore:  
Therefore:  
<br>
<br>
<math>\breve{T}=L(V)=\frac{C}{{{U}^{n}}}{{e}^{\tfrac{B}{V}}}</math>
<math>\breve{T}=L(V)=\frac{C}{{{U}^{n}}}{{e}^{\tfrac{B}{V}}}</math>
<br>
<br>
or:  
or:  
<br>
<br>
<math>{{e}^{{{\overline{T}}^{\prime }}}}=\frac{C}{{{U}^{n}}}{{e}^{\tfrac{B}{V}}}</math>
<math>{{e}^{{{\overline{T}}^{\prime }}}}=\frac{C}{{{U}^{n}}}{{e}^{\tfrac{B}{V}}}</math>
<br>
<br>
Thus:  
Thus:  
<br>
<br>
<math>{{\overline{T}}^{\prime }}=\ln (C)-n\ln (U)+\frac{B}{V}</math>
<math>{{\overline{T}}^{\prime }}=\ln (C)-n\ln (U)+\frac{B}{V}</math>
<br>
<br>
Substituting Eqn.(TV-logn-mean)into Eqn. (TV-logn-pdf) yields the T-NT lognormal model  <math>pdf</math> or:
Substituting Eqn.(TV-logn-mean)into Eqn. (TV-logn-pdf) yields the T-NT lognormal model  <math>pdf</math> or:
<br>
<br>
<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>
<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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| align="center" valign="middle" | [http://reliawiki.com/index.php/Template:TNT_Lognormal TNT Lognormal]
| valign="middle" | [http://reliawiki.com/index.php/Template:TNT_Lognormal TNT Lognormal]
 
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Revision as of 22:05, 10 February 2012

Webnotes-alta.png
Standard Folio Data TNT-Lognormal
ALTA

The T-NT lognormal model [math]\displaystyle{ pdf }[/math] can be obtained first by setting [math]\displaystyle{ \overline{T}=L(V) }[/math] in Eqn. (Temp-Volt).
Therefore:
[math]\displaystyle{ \breve{T}=L(V)=\frac{C}{{{U}^{n}}}{{e}^{\tfrac{B}{V}}} }[/math]
or:
[math]\displaystyle{ {{e}^{{{\overline{T}}^{\prime }}}}=\frac{C}{{{U}^{n}}}{{e}^{\tfrac{B}{V}}} }[/math]
Thus:
[math]\displaystyle{ {{\overline{T}}^{\prime }}=\ln (C)-n\ln (U)+\frac{B}{V} }[/math]
Substituting Eqn.(TV-logn-mean)into Eqn. (TV-logn-pdf) yields the T-NT lognormal model [math]\displaystyle{ pdf }[/math] or:
[math]\displaystyle{ 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]

TNT Lognormal


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