Comments on: A little bit about Heavy Tails and Black Swans and Stable Distributions http://dsanalytics.com/dsblog/a-little-bit-about-heavy-tails-and-black-swans-and-stable-distributions_76 Data Analytics- the art and science of analyzing data Sun, 06 Jul 2008 04:22:18 +0000 http://wordpress.org/?v=2.0.1 by: John Aitchison http://dsanalytics.com/dsblog/a-little-bit-about-heavy-tails-and-black-swans-and-stable-distributions_76#comment-47 Wed, 20 Jun 2007 11:08:04 +0000 http://dsanalytics.com/dsblog/a-little-bit-about-heavy-tails-and-black-swans-and-stable-distributions_76#comment-47 sorry, forgot the link http://www.gnxp.com/blog/2007/04/commonness-of-40-sd-events.php sorry, forgot the link
http://www.gnxp.com/blog/2007/04/commonness-of-40-sd-events.php

]]> by: John Aitchison http://dsanalytics.com/dsblog/a-little-bit-about-heavy-tails-and-black-swans-and-stable-distributions_76#comment-46 Wed, 20 Jun 2007 11:07:18 +0000 http://dsanalytics.com/dsblog/a-little-bit-about-heavy-tails-and-black-swans-and-stable-distributions_76#comment-46 Taleb is not without his critics – see, for example The Black Swan by Nassim Taleb: A Book Review at Mahalanobis http://mahalanobis.twoday.net/stories/3628077/ . The commonness of 40-SD events GeneExpression asks How often should we expect to observe events that are 40 standard deviations above the mean? Probably not ever. If we do observe such events more frequently than never, that may be because our initial guess was based on an incorrect model. One easy way for extreme events to be more common than seems plausible is if several variables are involved which interact multiplicatively with each other. To understand some key differences between an additive vs. multiplicative scenario, consider rolling three 6-sided dice, each numbered 0 - 5, with each face equally likely and each die independent of the others. Suppose in Game A we record the “score” as the sum of the numbers showing, while in Game B we record their product. This is very worth while following through as an illustration that interactions can produce outliers/improbable events. Taleb is not without his critics – see, for example The Black Swan by Nassim Taleb: A Book Review at Mahalanobis http://mahalanobis.twoday.net/stories/3628077/ .

The commonness of 40-SD events

GeneExpression asks

How often should we expect to observe events that are 40 standard deviations above the mean?

Probably not ever. If we do observe such events more frequently than never, that may be because our initial guess was based on an incorrect model.

One easy way for extreme events to be more common than seems plausible is if several variables are involved which interact multiplicatively with each other. To understand some key differences between an additive vs. multiplicative scenario, consider rolling three 6-sided dice, each numbered 0 - 5, with each face equally likely and each die independent of the others. Suppose in Game A we record the “score” as the sum of the numbers showing, while in Game B we record their product.

This is very worth while following through as an illustration that interactions can produce outliers/improbable events.

]]>