Other Types of Stability
The above concept of stability is based on the idea of a class of distributions being closed under a given set of operations on random variables, where the operation is "summation" or "averaging". Other operations that have been considered include:
- geometric stability: here the operation is to take the sum of a random number of random variables, where the number has a geometric distribution. The counterpart of the stable distribution in this case is the geometric stable distribution
- Max-stability: here the operation is to take the maximum of a number of random variables. The counterpart of the stable distribution in this case is the generalized extreme value distribution, and the theory for this case is dealt with as extreme value theory. See also the stability postulate. A version of this case in which the minimum is taken instead of the maximum is available by a simple extension.
Read more about this topic: Stability (probability)
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