most bell curves have thick tails

"Most bell curves have thick tails", by Bart Kosko (via MR) is a must-read. Main points:

* a great deal of science and engineering assumes a normal (Gaussian) distribution far too quickly.

* there are many bell curves. The Gaussian is rather thin-tailed, when compared with real-world distributions. It is the thinnest-tailed in the family of stable distributions.

* I quote:

the classical central limit theorem [link mine] result rests on a critical assumption that need not hold and that often does not hold in practice. The theorem assumes that the random dispersion about the mean is so comparatively slight that a particular measure of this dispersion — the variance or the standard deviation — is finite or does not blow up to infinity in a mathematical sense. Most bell curves have infinite or undefined variance even though they have a finite dispersion about their center point. The error is not in the bell curves but in the two-hundred-year-old assumption that variance equals dispersion. It does not in general.

* Standard deviation as a measure of dispersion is a dogma. Squaring means you weigh outliers too heavily.