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From the central limit theorem to heavy-tailed distributions

Part of: Distribution theory - Probability Stochastic processes Distribution theory Limit theorems

Published online by Cambridge University Press:  14 July 2016

Jinwen Chen
Jinwen Chen*
Affiliation:
Tsinghua University
*
∗Postal address: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China. Email address: [email protected]
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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

Heavy-tailed distributionpower lawcentral limit theoremrandomly indexed product

MSC classification

Primary: 60E05: Distributions 60F15: Strong theorems 60F99: None of the above, but in this section 60G50: Sums of independent random variables; random walks
Secondary: 62E10: Characterization and structure theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 40 , Issue 3 , September 2003 , pp. 803 - 806
Copyright
Copyright © Applied Probability Trust 2003 

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