Re: Simple Eval Question

*To*: mathgroup at smc.vnet.net*Subject*: [mg31889] Re: [mg31883] Simple Eval Question*From*: BobHanlon at aol.com*Date*: Mon, 10 Dec 2001 06:14:27 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

In a message dated 12/9/01 6:50:44 AM, ivo.welch at anderson.ucla.edu writes: >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.) > Solve is primarily for polynomials; use FindRoot. Needs["Graphics`Colors`"]; Needs["Statistics`ContinuousDistributions`"]; Clear[fd, pe, q]; fd[x_]:=Evaluate[PDF[LogNormalDistribution[0,1], x]]; W=1; g=0.5; V=2; pe[q_] := (p /. FindRoot[Integrate[((W+(x-p)*q)^g)/g*fd[x], {x, 0, Infinity}] == V, {p, 1.64-0.901q+1.11q^2}]); The starting value expression (quadratic estimate of p as a function of q) is developed below. pe[0.1] 1.56521 data = Table[{q, pe[q]}, {q, 0.02, 0.2, 0.02}]; quadEst[q_] := Evaluate[Fit[data,{1,q,q^2},q]]; Plot[quadEst[q], {q, 0.02, 0.2}, PlotStyle -> Blue, Epilog -> {Red, AbsolutePointSize[4], Point /@ data}]; Bob Hanlon Chantilly, VA USA