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No, standard deviation is special. If you have a large enough amount of independent distributions which gets averaged or added in some way, then the only thing
by username90 7y ago
No, standard deviation is special. If you have a large enough amount of independent distributions which gets averaged or added in some way, then the only thing which matters are their standard deviations and average values for what the final distribution looks like.
- darkerside 7y agoI'm well out of my wheelhouse, so anyone else chiming in would be appreciated. I'm not sure what you mean by "looks like", but I would imagine other "nonstandard" measures of deviation would also result in a consistent model. My larger point is that, something can be arbitrary and still be meaningful. If people agree on a common meaning, it formalizes a communication protocol that allows for much better information sharing.
- username90 7y ago"Looks like" as in the difference approaches zero as the number of times approaches infinity. This means that any distribution with standard deviation of X will behave as a normal distribution with standard deviation X when you have enough of them. Or in other words, any distribution with standard deviation of X will behave like any other distribution with standard deviation of X when you have enough of them. There is no other measure like this as there is no other equivalent to the central limit theorem. Therefore it makes sense to have this as a universal measure of random processes.