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I meant geometric mean...

"It's the statue, man, The Statue."
by Migeru (migeru at eurotrib dot com) on Sun Mar 25th, 2007 at 05:00:06 PM EST
[ Parent ]
Oh ... hey, that's the one I posted!

I did the arithmatic mean first, but it is just the sum scaled by a factor of 0.5. But since the central place hierarchy tends to be a log-linear relationship, the geometric mean felt like it was probably better.

And who knows ... one day in the distant past I may have actually read some literature that suggested that the geometric mean is the preferable measure in general for this situation ... I definitely knew a lot more abstract regional economics stuff a decade ago, even if I knew a lot less about the real world problems of fighting for better public transport.

I've been accused of being a Marxist, yet while Harpo's my favourite, it's Groucho I'm always quoting. Odd, that.

by BruceMcF (agila61 at netscape dot net) on Mon Mar 26th, 2007 at 10:02:48 AM EST
[ Parent ]
The geometric mean is better for quantities that are necessarily positive (like population), or that grow multiplicatively (like population).

"It's the statue, man, The Statue."
by Migeru (migeru at eurotrib dot com) on Mon Mar 26th, 2007 at 10:04:55 AM EST
[ Parent ]
Maybe ... I'm more a picking the tool to fit the problem kind of economist, so I would say that in this case, that fact that the size of the other city in the pair is a main factor in determing the percentage market share leads one into the logarithmic family. Its a main reason why the ratio of populations between adjoining levels of the central place hierarchy tends to be close to constant (for most developed economies). And in the logarithmic family, the simplest mean is:

antilog( (log(x1)+log(x2))/2 )

which in direct arithmatic is:

(x1*x2)^.5

I've been accused of being a Marxist, yet while Harpo's my favourite, it's Groucho I'm always quoting. Odd, that.

by BruceMcF (agila61 at netscape dot net) on Mon Mar 26th, 2007 at 11:03:05 AM EST
[ Parent ]
Exactly.

"It's the statue, man, The Statue."
by Migeru (migeru at eurotrib dot com) on Mon Mar 26th, 2007 at 05:34:49 PM EST
[ Parent ]

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