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Re: Simple Eval Question
*To*: mathgroup at smc.vnet.net
*Subject*: [mg31901] Re: [mg31883] Simple Eval Question
*From*: Andrzej Kozlowski <andrzej at tuins.ac.jp>
*Date*: Mon, 10 Dec 2001 06:14:45 -0500 (EST)
*Sender*: owner-wri-mathgroup at wolfram.com
In[1]:=
<<Statistics`ContinuousDistributions`
In[2]:=
W=1; g=0.5; q=0.1; V=2;
In[3]:=
fd[x_]:= PDF[ LogNormalDistribution[0,1],x ] ;
In[4]:=
FindRoot[
Evaluate[Integrate[ ((W +(x-p)*q)^g)/g * fd[x], { x, 0,
Infinity } ]==
V], {p ,1}]//Timing
Out[4]=
{30.93 Second,{p->1.56521}}
Somewhat surprisingly you can get the right answer also using NIntegrate
and much faster although with some error messages:
In[5]:=
FindRoot[
Evaluate[NIntegrate[ ((W +(x-p)*q)^g)/g * fd[x], { x, 0,
Infinity } ]==
V], {p ,1}]//Timing
Out[5]=
{0.45 Second,{p->1.56521}}
Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.u-tokyo.ac.jp/andrzej/
On Sunday, December 9, 2001, at 08:07 PM, ivo welch wrote:
> 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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