Comments on: Achievement is not normal

By: The single big jump principle — The Endeavour

The single big jump principle — The Endeavour — Tue, 09 Aug 2011 11:06:53 +0000

[...] It’s not true at all if your jumps have a thin-tailed distribution. But sometimes the payoffs in life’s games are [...]

By: John M

John M — Tue, 14 Jun 2011 20:44:04 +0000

Kragen is right generally. Extreme values from the normal are demonstrably Gumbel distributed.

By: Ankit Dangi

Ankit Dangi — Tue, 14 Jun 2011 18:25:19 +0000

Beautifully articulated. I liked the analogy of book readership, and the way the discussion has been presented about Achievement being non-normal and appearing as log-normal.

By: John W

John W — Tue, 22 Feb 2011 05:36:40 +0000

Measurements of physical growth such as height are log normal so her very first example of a normal distribution is wrong. The idea is good but in reality, most things are a combination of normal and log normal distribution in that there are additive as well as multiplicative components. Of course, the multiplicative components should dominate so most things are more accurately modeled with a log normal distribution than a normal distribution. Of course, all of these distributions are inherently wrong, they assume an infinite number of factors, yes there is a large number of factors but it isn’t infinite.

One important aspect of log normal is that it’s undefined for X less than zero, in other words, it starts at zero and goes to infinity whereas normal distribution is from minus infinity to positive infinity. Mean times to repair should be analyzed as log normal distribution since it’s not likely to be a negative value, obviously not all factors affecting time to repair are multiplicative but that very critical nature of starting at zero makes a world of difference.

Good topic for a speech but terrible research and content.

By: Kragen Javier Sitaker

Kragen Javier Sitaker — Thu, 08 Oct 2009 22:09:36 +0000

I would expect individual wealth to follow a Zipf distribution — but that’s not a “distribution” in the sense of a probability distribution. What kind of pdf would produce a Zipf distribution? I’m too ignorant to know.

By: John

John — Tue, 29 Sep 2009 22:18:21 +0000

I don’t take this too seriously; it’s just a plausibility argument.

By: gappy

gappy — Tue, 29 Sep 2009 22:14:08 +0000

I’d like to see the data showing conclusively that achievement is log-normally distributed. Many people are happy with the assumption that equity return are lognormal, but they are not. Perhaps “achievement” is better described by a gamma distribution, which is very flexible and has desirable scaling properties.

Incidentally, sometimes the term “long tail” is used interchangeably by “heavy tail”. But log-normal r.v.s are not heavy-tailed, and that jibes with intuition: if that were the case for achievement, then with high probability the advances to any given field who be contributed by a single individual.

By: Ken

Ken — Tue, 29 Sep 2009 21:22:08 +0000

Most distributions aren’t anything at all. There are some distributions that allow arbitrary skewness and kurtosis and these seem the best option for tail probabilities, for when you need something like that, for example child growth.

I’ve wiped all the silly examples about normal probabilities from my service stats course. Questions like the time to do something is normal mean 10s sd 2 s, what is the probability that someone will finish in 9s. I do talk about means, the central limit theorem does work well.

By: Other things that aren’t normal… « The Idea

Other things that aren’t normal… « The Idea — Tue, 29 Sep 2009 18:57:39 +0000

[...] rants aside, here’s a very interesting look at human achievement: http://www.johndcook.com/blog/2009/09/29/achievement-is-log-normal/. Its an interesting read just for the statistics. And probably one of the better explanations of [...]