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MathGroup Archive 2003

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Re: Alternative to bivariate Taylor series

  • To: mathgroup at smc.vnet.net
  • Subject: [mg44651] Re: Alternative to bivariate Taylor series
  • From: "Steve Luttrell" <luttrell at _removemefirst_westmal.demon.co.uk>
  • Date: Wed, 19 Nov 2003 04:59:16 -0500 (EST)
  • References: <bpd2a7$ce5$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

You can do this by numerical integration as follows (insert whatever means
and standard deviations you need in the Gaussian PDFs):

In[11]:=
a = NIntegrate[Log[1 + Exp[x - y]]*Exp[-x^2]*Exp[-y^2],
   {x, -Infinity, Infinity}, {y, -Infinity, Infinity}]
Out[11]=
2.53231

In[12]:=
b = NIntegrate[Exp[-x^2]*Exp[-y^2], {x, -Infinity, Infinity},
   {y, -Infinity, Infinity}]
Out[12]=
3.14159

In[13]:=
a/b
Out[13]=
0.806059

--
Steve Luttrell
West Malvern, UK

"koshi man" <man_koshi at yahoo.com> wrote in message
news:bpd2a7$ce5$1 at smc.vnet.net...
> Is there any expansion to log(1+exp(x-y)) other than
> Taylor series in the integer powers of x and y ?
>
> I'm trying to find expectation of above function given
> x, y are random variables with gaussian distributions
> of known  mean and variances.
>
> What about other bivariate expansions in Mathematica?
>
> CK
>
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