Re: Bivariate Normal Distributions -- can they be estimated in my lifetime?
- To: mathgroup at smc.vnet.net
- Subject: [mg14824] Re: Bivariate Normal Distributions -- can they be estimated in my lifetime?
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Wed, 18 Nov 1998 01:29:29 -0500
- Organization: University of Western Australia
- References: <firstname.lastname@example.org>
- Sender: owner-wri-mathgroup at wolfram.com
Luci Ellis wrote:
> I have given up on several weeks of work trying to do maximum likelihood
> estimation of a bivariate probit model (ie two binary decisions that
> are correlated). The likelihood function itself is easy to construct,
> and in principle should be easy to maximise (using FindMinimum on its
> negative) because the PDF of the bivariate normal distribution is
> However, it appears impossible to do this on a desktop computer.
I have written a short Notebook on a number of ways for computing the
PDF of the bivariate normal distribution. It is available at
> Chris Farr has previously suggested using a discrete approximation of
> the CDF, but I am concerned that the approximation error would get too
> large, making my results unreliable.
Possibly -- but how accurately do you need the PDF?
> Gauss and Stata can both do this -- why can't Mathematica?
An interesting question: "How accurate are the PDF produced using these
> I accept that a general package like Mathematica is going to be slower
> than a specialised package like Stata or Shazam -- but the margin needs
> to be smaller if Mathematica is to be usable in this context.
I think Mathematica certainly _is_ usable in this context!
Paul Abbott Phone: +61-8-9380-2734
Department of Physics Fax: +61-8-9380-1014
The University of Western Australia Nedlands WA 6907
mailto:paul at physics.uwa.edu.au AUSTRALIA
God IS a weakly left-handed dice player
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Many data points = frustration