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Short Communications

A reparametrization of the symmetric $\alpha$-stable distributions and their dispersive ordering

R. Zieliński

Institute of Mathematics, Polish Academy of Sciences, Poland

Abstract: A reparametrization of symmetric $\alpha$-stable distributions is proposed such that the ordering of distributions according to the value of parameters amounts to their dispersive ordering. A statistical application is presented.

Keywords: symmetric stable distributions, characteristic exponent, index of stability, dispersive ordering, Fama–Roll estimator.

Received: 16.04.1999

Language: English

DOI: 10.4213/tvp475

 English version: Theory of Probability and its Applications, 2001, 45:2, 357–358

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