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Derived distribution

Posted 9 years ago

Hi everyone! I'm trying do obtain the derived distribution of Q [P,EP] I know the distribution of both P and EP Here attached the code that I'm using. It runs forever...:-( Thanks!

POSTED BY: hydroviolante
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For the distribution to be valid, you need to ask for a distribution of a quantity that is a number or vector for a fixed value of r, whereas you are asking for the trajectory. Perhaps you need to sample the function at multiple instances of times, and then ask for the distribution.

It needs to be set, that DSolve, provided all variable are symbolic can find an analytic solution:

(* try this *)

Zt = DSolve[{-z'[t] == ((
     r \[Eta]) (\[Rho] \[Alpha] g r z[t] - 2 cos\[Theta] \[Gamma]))/(
   8 z[t]), z[0] == L}, z, t]

The solution is real for numeric values of his and for some r and t, but it may only represent a branch of the global solution. Then something like

 TransformedDistribution[Re[z[1.]] /. First[Zt] /. subst,
  r \[Distributed] NormalDistribution[\[Mu], \[Sigma]] /. subst],
 10^5], PlotRange -> All]

works, but shows that the solution is not likely to be a global one, since it has imaginary part.

Hence, you can use ParametricNDSolve too.

POSTED BY: Oleksandr Pavlyk
Posted 9 years ago

Thanks for updating your post with a Mathematica notebook. That makes it much easier for someone to help.

POSTED BY: Jim Baldwin
Posted 9 years ago

What you've posted isn't exactly in Mathematica format (and I suspect that you probably want lowercase Greek letters rather than uppercase). I think you'll get more help if you use the Code sample icon (left-most unlabeled icon - a blank page with < >) and/or attach a Mathematica notebook.

POSTED BY: Jim Baldwin
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