From the central limit theorem to heavy-tailed distributions
- 1 September 2003
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 40 (3) , 803-806
- https://doi.org/10.1239/jap/1059060906
Abstract
It has been observed that in many practical situations randomly stopped products of random variables have power law distributions. In this note we show that, in order for such a product to have a power law distribution, the only random indices are the exponentially distributed ones. We also consider a more general problem, which is closely related to problems concerning transformation from the central limit theorem to heavy-tailed distributions.Keywords
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