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The T-NT lognormal model [math]\displaystyle{ pdf }[/math] can be obtained first by setting [math]\displaystyle{ \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{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]
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