Re: [R] integrate lgamma from 0 to Inf
I am late to this discussion so forgive me if I am being redundant. It
appears to me that the integral from 0 to infinity of log-gamma may
diverge to infinity. Equation 6.1.50 of Abramowitz Stegun shows that a
re-expression of lnGamma(x) and the Stirling approximation involves
(x-1/2)*log(x) -x along with other terms. This term appears to dominate
the integral and itself diverge. It is worth checking out.
integrate(lgamma, lower = 0, upper = 10)
43.24636 with absolute error 1.6e-11
integrate(lgamma, lower = 0, upper = 100)
15438.12 with absolute error 1.4
integrate(lgamma, lower = 0, upper = 1000)
2701843 with absolute error 254
integrate(lgamma, lower = 0, upper = 1)
385485116 with absolute error 18464
gterm - function(x){(x-.5)*log(x)-x}
integrate(gterm,lower=0,upper=10)
33.61633 with absolute error 1.1e-05
integrate(gterm,lower=0,upper=100)
15345.59 with absolute error 1.2
integrate(gterm,lower=0,upper=1000)
2700923 with absolute error 252
integrate(gterm,lower=0,upper=1)
385475926 with absolute error 18462
Joseph F. Lucke
Senior Statistician
Research Institute on Addictions
University at Buffalo
State University of New York
1021 Main Street
Buffalo, NY 14203-1016
Office: 716-887-6807
Fax: 716-887-2510
http://www.ria.buffalo.edu/profiles/lucke.html
Andreas Wittmann andreas_wittm...@gmx.de
Sent by: r-help-boun...@r-project.org
04/22/2009 03:28 AM
To
r-help@r-project.org
cc
Subject
[R] integrate lgamma from 0 to Inf
Dear R users,
i try to integrate lgamma from 0 to Inf. But here i get the message
roundoff error is detected in the extrapolation table, if i use 1.0e120
instead of Inf the computation works, but this is against the suggestion
of integrates help information to use Inf explicitly. Using stirlings
approximation doesnt bring the solution too.
## Stirlings approximation
lgammaApprox - function(x)
{
0.5*log(2*pi)+(x-(1/2))*log(x)-x
}
integrate(lgamma, lower = 0, upper = 1.0e120)
integrate(lgammaApprox, lower = 0, upper = 1.0e120)
integrate(lgamma, lower = 0, upper = 1.0e120)
1.374051e+242 with absolute error 3.2e+235
integrate(lgammaApprox, lower = 0, upper = 1.0e120)
1.374051e+242 with absolute error 3.2e+235
integrate(lgamma, lower = 0, upper = Inf)
integrate(lgammaApprox, lower = 0, upper = Inf)
integrate(lgamma, lower = 0, upper = Inf)
Fehler in integrate(lgamma, lower = 0, upper = Inf) :
roundoff error is detected in the extrapolation table
integrate(lgammaApprox, lower = 0, upper = Inf)
Fehler in integrate(lgammaApprox, lower = 0, upper = Inf) :
roundoff error is detected in the extrapolation table
Many thanks if you have any advice for me!
best regards
Andreas
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Re: [R] integrate lgamma from 0 to Inf
On Wed, Apr 22, 2009 at 3:28 AM, Andreas Wittmann andreas_wittm...@gmx.de wrote: i try to integrate lgamma from 0 to Inf. Both gamma and log are positive and monotonically increasing for large arguments. What can you conclude about the integrability of log(gamma(x))? -s __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] integrate lgamma from 0 to Inf
IMHO, you should consult an advanced text on calculus with integration over infinite intervals, so that you understand what you are trying to do. Joseph F. Lucke Senior Statistician Research Institute on Addictions University at Buffalo State University of New York 1021 Main Street Buffalo, NY 14203-1016 Office: 716-887-6807 Fax: 716-887-2510 http://www.ria.buffalo.edu/profiles/lucke.html Stavros Macrakis macra...@alum.mit.edu Sent by: r-help-boun...@r-project.org 04/27/2009 10:30 AM To Andreas Wittmann andreas_wittm...@gmx.de cc r-help@r-project.org Subject Re: [R] integrate lgamma from 0 to Inf On Wed, Apr 22, 2009 at 3:28 AM, Andreas Wittmann andreas_wittm...@gmx.de wrote: i try to integrate lgamma from 0 to Inf. Both gamma and log are positive and monotonically increasing for large arguments. What can you conclude about the integrability of log(gamma(x))? -s __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. [[alternative HTML version deleted]] __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
[R] integrate lgamma from 0 to Inf
Dear R users,
i try to integrate lgamma from 0 to Inf. But here i get the message roundoff
error is detected in the extrapolation table, if i use 1.0e120 instead of Inf
the computation works, but this is against the suggestion of integrates help
information to use Inf explicitly. Using stirlings approximation doesnt bring
the solution too.
## Stirlings approximation
lgammaApprox - function(x)
{
0.5*log(2*pi)+(x-(1/2))*log(x)-x
}
integrate(lgamma, lower = 0, upper = 1.0e120)
integrate(lgammaApprox, lower = 0, upper = 1.0e120)
integrate(lgamma, lower = 0, upper = 1.0e120)
1.374051e+242 with absolute error 3.2e+235
integrate(lgammaApprox, lower = 0, upper = 1.0e120)
1.374051e+242 with absolute error 3.2e+235
integrate(lgamma, lower = 0, upper = Inf)
integrate(lgammaApprox, lower = 0, upper = Inf)
integrate(lgamma, lower = 0, upper = Inf)
Fehler in integrate(lgamma, lower = 0, upper = Inf) :
roundoff error is detected in the extrapolation table
integrate(lgammaApprox, lower = 0, upper = Inf)
Fehler in integrate(lgammaApprox, lower = 0, upper = Inf) :
roundoff error is detected in the extrapolation table
Many thanks if you have any advice for me!
best regards
Andreas
--
__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
