power law

It’s not a pyramid!

Posted on October 11, 2010 by Tara Thiagarajan in Uncategorized. 4 comments

CK Prahalad’s book The Fortune at the Bottom of the Pyramid has firmly established our visual impression of how incomes are distributed as a pyramid. A strong, solid structure with the poorest at the bottom that slowly tapers, kind of holding up the apex. In reality it looks NOTHING like a pyramid. Here’s a 3D visualization of what it looks like based on real income distributions. Of course, if I had a lot of time on my hands I’d figure out how to plot it in 3D a lot better, maybe starting with a square shape rather than a circle so it compares better to a pyramid. But I don’t. You get the picture though. (To get more of a sense for what income distributions are like check out my earlier posts Who Cares about the … Read More »

The Tales of Tails

Posted on March 19, 2010 by Tara Thiagarajan in Uncategorized. Comments Off on 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 … Read More »

Income Distributions around the World

Posted on March 19, 2010 by Tara Thiagarajan in Uncategorized. Comments Off on Income Distributions around the World

In my last, and much lighter post Who cares about the average income! I talked about the heavy tailed nature of income distributions. Here’s a link to some actual income distributions for the USA, India, Japan and France (scroll all the way to page 3 and look at Figure 1 on that page). Of course, the data for India includes only that of taxpayers and most of India has insufficient income to pay taxes so this is grossly misrepresentative. And unfortunately, the authors also note that the Indian data, even for taxpayers, is incomplete relative to the other countries for the reason that: “In spite of the best of our efforts in collecting the equivalent data from the Income Tax Department of the Government of India or the Reserve Bank of India, we are unable to give … Read More »

Who cares about the average income!

Posted on March 17, 2010 by Tara Thiagarajan in Blog, Writing. Comments Off on Who cares about the average income!

Many of us think of statistics as basically taking the average of some numbers. Maybe we even think of the normal distribution or ‘the bell curve’ and the concept of standard deviation. In this context, if you say the average height of people in India is around 5’ 5” with a standard deviation of 5”, it’s pretty intuitive what that means – that when you arrive in India you will find most people around 5’5” with some variation this way and that way of mostly 5”. In large part we all look similar and can fit in the same seats, sleep on the same size beds and fit through the same doorways. Instead, imagine if the distribution was not a bell curve but rather looked like this. A decreasing function with a heavy tail.

What this would mean is that most … Read More »