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MathGroup Archive 2007

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Re: Numerical Integrate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72883] Re: [mg72864] Numerical Integrate
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Wed, 24 Jan 2007 05:30:04 -0500 (EST)
  • Reply-to: hanlonr at cox.net

Needs["Statistics`"];

f1[x_]=PDF[NormalDistribution[0, 1],x];

f2[x_]=PDF[LogNormalDistribution[0, 1],x];

convolve[f_,g_, t_?NumericQ]:=
    NIntegrate[f[u]*g[t-u],{u,0,t}];

NIntegrate[convolve[f1,f2,t],{t,-Infinity,0}]//Re

0.5

NIntegrate[convolve[f1,f2,t],{t,-Infinity,Infinity}]//Re

1.


Bob Hanlon

---- "mailcwc at gmail.com" <mailcwc at gmail.com> wrote: 
> I need to perform the following integration:
> 
> Integrate[  Convolution[G(t), X(t)], {t, -inf, 0}],
> 
> where G is Normal distribution, and X is Log-normal distribution.
> 
> As I know, there is no analytical form for the convolution.
> I tried NIntegrate to perform numerical calculation, but Mathematica
> can't accept it.
> Does anyone know how to deal such problem?
> 


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