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MathGroup Archive 2007

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Re: Numerical Integrate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72888] Re: Numerical Integrate
  • From: "Robert Dodier" <robert.dodier at gmail.com>
  • Date: Wed, 24 Jan 2007 05:50:12 -0500 (EST)
  • References: <ep4jvt$pam$1@smc.vnet.net>

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.

One way to approach this is to approximate the convolution via the
fast Fourier transform: discretize G and X, then compute the inverse
transform of FFT(G) times FFT(X) pointwise; that yields an
approximation
of the density of the convolution. Then sum up the tail that's to the
left
of 0 to approximate the integral you want.

That's probably not too accurate (because you have to cut off the
tails of G and X, and discretize) but it is easy and fast.

Hope this helps.

Robert Dodier


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