From: Spencer Graves <spencer.graves_at_pdf.com>

Date: Tue 21 Jun 2005 - 00:53:47 EST

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Tue Jun 21 00:56:33 2005

Date: Tue 21 Jun 2005 - 00:53:47 EST

If I read your question correctly, you want to integrate the indicated expression over x = 0 to Inf. If I substitute z = x/sqrt(b), your integral becomes one constant plus another times the expected value of (y-z/sqrt(b))^2, where z follows Student's t with v degrees of freedom. Expand the quadratic form to get y^2 + (Ez^2)/b and find something that gives the variance of Student's t.

I don't have time now to work out the details, but this should work if I've understood your question correctly.

spencer graves

Clark Allan wrote:

> hi all

*>
**> at the outset i must APOLOGIZE for sending the following mail. it is not
**> R related but since there are many stats and maths buffs that use the
**> list i decided to send the following question.
**>
**> integrate ((1+((y-bx)^2)/(av))*(1+(x^2)/(bv)))^(-0.5*(v+1))
**>
**> over the interval 0 to inf
**>
**>
**> a>0, b>0 and v>4
**> y treated as a constant over the real line.
**>
**> i could integrate the function using "integrate". do so for a large
**> number of y values and plot the function BUT i would prefer an exact
**> solution if possible.
**>
**> any help will be appreciated.
**> i've attached a word file with the formula
**>
**>
**> \
**> allan
**>
**>
**> ------------------------------------------------------------------------
**>
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*

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Tue Jun 21 00:56:33 2005

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