Talk:Gauss–Kuzmin distribution

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[edit] Recherches Arithmétiques in Gauss-Kuzmin distribution

Copied from User talk:Linas:

You added Recherches Arithmétiques as a reference to Gauss-Kuzmin distribution a couple of years back. I wondered where you found this. Unfortunately, I don't have access to the original, and I couldn't find it in skimming the Gauss' Collected Works (Werke Sammlung). I'd love to confirm the reference — for example, giving a page number — but I can't seem to, so I'm curious how you did. Thanks, Calbaer 15:50, 12 May 2007 (UTC)

Linas will hopefully be able to give a more complete reply. All I can tell you is that Recherches Arithmétiques is a translation in French of Disquisitiones Arithmeticae. [1] -- Jitse Niesen (talk) 03:31, 13 May 2007 (UTC)

I'm pretty sure that observation was not made in Disquisitiones Arithmeticae. According to Kuzmin's original paper, it was made in a letter to Laplace written after Disquisitiones Arithmeticae was published. According to Knuth (TAOCP v.2 ed.2 p.347), prior to that it was merely in his notebook. Kuzmin says that the letter is in volume 10 of the complete works, and, after poking around a fair bit, I found an entry in Gauss' "journal with explanations" on pp. 552-556 of Band 10, Abt 1 (of the edition linked above). The reference should be modified accordingly, unless there's also a mention of it in Disquisitiones Arithmeticae as well (which, again I doubt). Calbaer 05:40, 13 May 2007 (UTC)

Although I am fortunate in having access to a very good library (UT Austin), I would not be able to verify the reference i.e. come up with a page number, without going there, and spending half a day crawling through the thing. Which is not something I feel like doing just now. I no longer recall what prompted me to put the Recherches Arithmétiques reference in there, I must have been hasty. We should, however, move this conversation to the talk page of that article. linas 17:53, 13 May 2007 (UTC)

Yes, the half-day at the library is what I wound up doing, though I came up somewhat empty before continuing the search online at night. (I wanted to have a solid reference for an academic paper.) Like I say, though, all references I can find seem to indicate it's elsewhere, and I'm afraid that the "Recherches Arithmétiques" reference has by now shown up in an academic paper, so I'll correct the link, and, if you find a reference in Disquisitiones Arithmeticae, you can correct my correction. Calbaer 22:10, 13 May 2007 (UTC)

[edit] Entropy

The page currently states that the entropy is 3.43... but surely this cannot be right; or, perhaps, some other definition of entropy is being used? A quick numerical calculation of

where

shows that

H = 2.379246...

although the sum is rather slow to converge ... Now one has that

but one does not normally define entropy with this extra factor of 2... oh, hmm. Appearently information-entropists, according to our wikipedia article do define their entropy with log_2. OK, whatever ... linas (talk) 20:33, 1 June 2008 (UTC)