Statistics Help?

[swestrup]

I've been wondering what sort of statistical distribution governs things like the ranking of countries by population. I've spend a bunch of hours trying to figure out if you get a well-known distribution curve by plotting these values on a bar graph, but so far I've not had any luck.

And naturally all of the statistical mathematics I've found on the subject assume far more knowledge of the subject than I have, and uses non-standard mathematical terminology to boot (statistics historically uses its own bizarre set of mathematical terms which don't mean the same as their counterparts in the rest of math.)

Does anyone on my f-list know enough to lend a hand?  What I'm basically trying to do here is to figure out how to generate this sort of table for a random world given a set population and a number of other (to be determined) input parameters.

Comments

[hendrikboom.livejournal.com]

Did you try Zipf's law? contents/size/probabliliyt proportional to the reciprocal of rank? It has the unfortunate mathematical property that the sum of 1/n as ngoes to infinity is infinite, but if you cutt off the tail it seems to fit well with experience in a lot of circumstances.

As Lambert Meertens expresesed it, If you classify any kind of thing into categories, and ramk the categories by the number of things in them, it'll turn out to be proportional to 1/n. Not sure if he was stating an empirical law of nature or just telling me what Zopf's law was, though.

[swestrup]

No, I didn't check out zipf's law as I concentrated on discrete distributions that summed to unity. Even then there were over a dozen. I'll check into it.

[sps.livejournal.com]

Yeah, actually it was a result that caused quite a stir in the lniguistics and textual analysis communities that Zipf's law is in some interesting sense vacuous....

[swestrup]

Okay, now I have tried Zipf's law and its a pretty close approximation to what I was looking for! Now if I can just figure out how to deal with the problem of things summing to much more than unity, I'll be set.

(My problem involves partitioning a known population into countries, thus the total needs to be fixed...)