Friday, March 19, 2010

The Tales of Tails

When we enter a space our natural inclination is to do a quick visual survey of who’s around. When we walk into a first grade classroom for instance, we expect to see a whole lot of 5 and 6 year olds and one or two adults.

Now if we were to plot the heights of the people in the room we would get a narrow ‘bell curve’ like distribution centred around 3.5’ and a point or two sticking out somewhere in the range of 5’and 6’.

Let’s say I wasn’t there and all I had in front of me was the distribution that you put down. I could pretty easily guess what kind of situation this was. Where else do you have a bunch of small people with just one large person? Now instead, what if I showed you a distribution that looked like this?

There are still thirty kids of the same size range. But now there are around 30 grown ups as well. Where would you find that kind of situation?

If you guessed that it was one of the kid’s 6th birthday parties, you would probably be right. So every distribution has a tale to tell. And the tale runs deeper. It tells us something about the nature of height itself. The bell shaped curve suggests that the height of one child in the class is virtually independent of the height of the others. Indeed for each of us, our heights play out from a highly similar genetic program with small variations arising from random environmental events.

It’s fairly easy to make sense of this kind of bell shaped distribution since we’ve all seen it in school. But what about the distribution of incomes? What tale does it tell? Why does it look so different? (To understand what income distributions look like, please read my earlier post Who cares about the average income!). These heavy tailed distributions and the power relationship that they often reflect, tells you that there’s no one size fits all, no meaningful ‘average’. More significantly they reveal a story of high interdependence, a story of a dynamically changing complex system. It is a reflection that my income does depend on yours in some very complex way. The distribution of income is a static view of a constantly changing interdependent process. Money is changing hands all the time and every so often we take a picture of how it is looks before it is passed on. This is fundamentally different from the story of the bell curve. And every small turn and kink in the distribution offers another twist to the tale.

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