# What are Gaussian Statistics?

1. Jan 2, 2016

### bballwaterboy

I heard a guy mention in a debate that some math calculation didn't obey Gaussian statistics. It was a debate re: the economy (not important here, though).

I was curious what was meant by "Gaussian statistics" and would appreciate if anyone could offer a sort of layman's definition. Thanks so much!

2. Jan 2, 2016

### andrewkirk

He was probably saying that some economic random variable did not have a Normal Distribution. The Normal Distribution is also known as the 'Bell Curve' as well as the 'Gaussian distribution' (because it was first invented by CF Gauss). Many random phenomena are assumed to be Normally Distributed because it makes calculations about them easier. But in some cases that assumption is very inaccurate, and that can cause big, unforeseen accidents.
The collapse of the hedge fund Long-Term Capital Management in 1998 is believed to have arisen from the fund managers assuming that certain economic variables were Normally Distributed when they were not.

3. Jan 4, 2016

### ElijahRockers

I'd be interested in reading more about that, but I didn't see much about it in the wiki.

4. Jan 4, 2016

### andrewkirk

This short article is more helpful, and points to a book by Benoit Mandelbrot all about the danger of the Gaussian assumption.

'Kurtosis' - the fourth moment of the distribution - measures how 'fat' the 'tails' of the distribution are. 'Excess kurtosis' is when there is more probability weight in the tails of a distribution than in a normal distribution with the same first two moments. Excess kurtosis - aka 'fat tails' - along with asymmetry (aka skew - related to the third moment) are problems that get a great deal of attention in finance these days, where it has belatedly been realised that testing the validity of assumptions of normality is very important.