Date:         Thu, 7 Jul 2005 13:28:49 -0400
Reply-To:     Richard Ristow <wrristow@MINDSPRING.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Richard Ristow <wrristow@MINDSPRING.COM>
Subject:      Re: precision & size limits
Comments: To: Walter Yaggins <niwiy@HOTMAIL.COM>
In-Reply-To:  <1120747010.394489.201340@g49g2000cwa.googlegroups.com>
Content-Type: text/plain; charset="us-ascii"; format=flowed

At 10:36 AM 7/7/2005, Walter Yaggins wrote:

>Thanks to all. It's a maximum likelihood function:
>
>maximize((a/b)^a*((c-a)(c-b))^(c-a))
>
>where a and b grow to be quite fairly large integers (in the 100s).

All right: this is the combinatorial case, as are likelihood functions
in general, and can generate immensely large or small numbers under
ordinary circumstances.

>I guess I have to do some math, and figure out how to scale it all
>down safely.

That may not work; combinatorial problems produce wide dynamic ranges,
not just large (or very small) magnitudes.

The usual solution is to maximize the log of the likelihood function

    a*(log(a)-log(b)) + (c-a)(log(c-a) + log (c-b))

(If I have the algebra right, which I don't, always.)

Is that more workable for you?