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Because many phenomena aren't in fact representations of arbitrary random variables. Take word distribution in any human language for instance. Word frequencie
by BjoernKW 9y ago
Because many phenomena aren't in fact representations of arbitrary random variables.
Take word distribution in any human language for instance. Word frequencies follow a Zipf distribution because it decreases entropy and hence is more efficient.
- oh_sigh 9y agoIt's not arbitrary random variables, it is independent additive variables which leads you to gaussian distributions frequently.
- pmiller2 9y agoThe surprising thing about the CLT is that it applies whenever the means and variances of the summed random variables exist. This is really a very mild condition, but the surprise to me is that the result is independent of the actual distributions of the variables being summed!
- pishpash 9y agoThe convergence rates are different though, so at finite sample sizes and as a practical matter, it does matter.