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MathGroup Archive 2001

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Re: Simple Eval Question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg31893] Re: Simple Eval Question
  • From: bghiggins at ucdavis.edu (Brian Higgins)
  • Date: Mon, 10 Dec 2001 06:14:33 -0500 (EST)
  • References: <9uvh6m$ibg$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Ivo,

You can use FindRoot:

<< Statistics`ContinuousDistributions`

W = 1; g = 0.5;  V = 2; q = 0.1;
fd[x_] := PDF[ LogNormalDistribution[0, 1], x ] ;
FindRoot[NIntegrate[ ((W + (x - p)*q)^g)/g * fd[x], { x, 0, Infinity } ] == 
    V, {p, 1, 2}]
{p -> 1.56521}

If you need to plot the solution as a function of q here is one way:

myfunc[s_] := 
  p /. FindRoot[
      NIntegrate[ ((W + (x - p)*s)^g)/g * fd[x], { x, 0, Infinity } ] == 
        V, {p, 1, 2}]
Plot[myfunc[s], {s, 0.1, .3}]

Cheers,

Brian

ivo.welch at anderson.ucla.edu (ivo welch) wrote in message news:<9uvh6m$ibg$1 at smc.vnet.net>...
> I have a simple problem.  I want to numerically solve
> 
>    Solve[  Integrate[ f[x,p]*g[x], {x,0,Infinity}] == V , p ]
> 
> where f[] and g[] are defined functions, but the naive solution fails.
> 
> W=1; g=0.5; q=0.1; V=2;
> fd[x_]:= PDF[ LogNormalDistribution[0,1],x ] ;
> Solve[ Integrate[ ((W +(x-p)*q)^g)/g * fd[x], { x, 0, Infinity } ]== V, p ]
> 
> Solve::"tdep": "The equations appear to involve the variables to be solved \
> for in an essentially non-algebraic way."
> 
> The correct answer seems to be 1.5652 .  How do I ask Mathematica to tell me
> this number?
> 
> (My ultimate goal is to plot the solved p as a function of q.)
> 
> /iaw


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