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

[sps.livejournal.com]

Well—what's the model? What is a ‘country’? I'm afraid fifteen seconds contemplation of that question leads me to believe that it's too chaotic to expect anything in particular. I'm not even sure that another planet would converge on the same formal notion of country that we seem to have. I suspect it's a legal fiction arising from the details of european history.

[hendrikboom.livejournal.com]

What's specific about European history here? Isn't it a matter of kings/warlords/emporers duking it out? Hasn't that been much the same everywhere there was enough subsistence to support an army?

[sps.livejournal.com]

I'm not so sure. Much of the world is much less obsessed by territory. Even in Scotland I'm not sure that the fealty model was so top-down. Clans that happen to inhabit a certain area might be part of an association or owe fealty to a laird, but that does not mean that the laird rules over the territory and could hand it to someone else, does it?

Tribal associations may be a natural, emergent human structure, but binding them to lines on a map and then letting those lines supercede the human relations seems quite European to me.

[sps.livejournal.com]

...And a consequence of the royal houses all being family and not ‘duking it out’ (except perhaps in the punning sense), but settling matters behind the scenes as business and social relations, not among the people but among the Families.

[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...)

[hendrikboom.livejournal.com]

I guess you just estimate how many countries you need, and there's your cutoff.

[swestrup]

My problem seems to be that I always run out of population long before I have anywhere near a reasonable number of countries. Still, I think I'm making progress.