3 ms·

> As a (former) astronomer, I've never understood why people assume normal distributions for everything. It shouldn't, because there is a big reason to lean to

by Kenji 9y ago

> As a (former) astronomer, I've never understood why people assume normal distributions for everything. It shouldn't, because there is a big reason to lean towards normal distribution, and that is the central limit theorem. If you sample a variety of different distributions, the sum of all these samples will go towards a normal distribution. That is why the normal distribution pops up in so many places.

smallnamespace 9y ago
That sounds nice, justifying why you expect your distribution to be the sum of other distributions, and not another operation like multiplication takes a lot more work; in some fields (e.g. finance), it's completely wrong.
- Houshalter 9y ago
  If you multiply random numbers together you get a log normal distribution. Which means the logarithm of the number is normally distributed (multiplication is just adding logarithms after all.) However multiplicative noise is a lot less common than additive noise.
antognini 9y ago
I understand that. But in astronomy, there are so many vastly different scales to work with, that in practice, at any particular scale, there is usually only one physical process that dominates. It is extremely unlikely for two independent physical processes to operate at nearly the same scale! So it's hard to get processes that are the sum of enough random variables to make a distribution approximately Gaussian. The situation is probably different in a field like biology because there are many factors that, say, affect a person's height. The closest that I've ever encountered in astronomy was the distribution of the powers of a class of radio galaxies I studied that exhibited an approximately log-normal distribution. (See figure 7 of [1].) [1]: http://adsabs.harvard.edu/abs/2012ApJ...756..116A http://adsabs.harvard.edu/abs/2012ApJ...756..116A
dnautics 9y ago
Central limit theorem only yields normality when the source distributions have defined variance, otherwise they go to levy alpha.
orionblastar 9y ago
They want everything to hit a Bell Curve because that is the only thing they remember from statistics class. I've had debates that not everything comes out as a Bell Curve only to be called an idiot for claiming that.

by Kenji 9y ago

smallnamespace 9y ago

That sounds nice, justifying why you expect your distribution to be the sum of other distributions, and not another operation like multiplication takes a lot more work; in some fields (e.g. finance), it's completely wrong.

Houshalter 9y ago
If you multiply random numbers together you get a log normal distribution. Which means the logarithm of the number is normally distributed (multiplication is just adding logarithms after all.) However multiplicative noise is a lot less common than additive noise.

antognini 9y ago

I understand that. But in astronomy, there are so many vastly different scales to work with, that in practice, at any particular scale, there is usually only one physical process that dominates. It is extremely unlikely for two independent physical processes to operate at nearly the same scale! So it's hard to get processes that are the sum of enough random variables to make a distribution approximately Gaussian. The situation is probably different in a field like biology because there are many factors that, say, affect a person's height. The closest that I've ever encountered in astronomy was the distribution of the powers of a class of radio galaxies I studied that exhibited an approximately log-normal distribution. (See figure 7 of [1].) [1]: http://adsabs.harvard.edu/abs/2012ApJ...756..116A http://adsabs.harvard.edu/abs/2012ApJ...756..116A

dnautics 9y ago

Central limit theorem only yields normality when the source distributions have defined variance, otherwise they go to levy alpha.

orionblastar 9y ago

They want everything to hit a Bell Curve because that is the only thing they remember from statistics class. I've had debates that not everything comes out as a Bell Curve only to be called an idiot for claiming that.