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August, 1981 Distribution of Symmetric Stable Laws of Index $2^{-n}$
Shashanka S. Mitra
Ann. Probab. 9(4): 710-711 (August, 1981). DOI: 10.1214/aop/1176994380

Abstract

Let $X_1, X_2 \cdots, X_n(n \geq 2)$ be independent standard normal. Then the random variable $U = X_1/V_n$ where $V_n = \exp_2\lbrack 2^{n - 2} - 1\rbrack X_2(X_3)^2 \cdots(X^2_n)^{2^{n - 3}} \quad n \geq 3 \\ = X_2 \text{for} n = 2$ has a symmetric stable distribution with index $2^{2 - n}$.

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Shashanka S. Mitra. "Distribution of Symmetric Stable Laws of Index $2^{-n}$." Ann. Probab. 9 (4) 710 - 711, August, 1981. https://doi.org/10.1214/aop/1176994380

Information

Published: August, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0461.60034
MathSciNet: MR624700
Digital Object Identifier: 10.1214/aop/1176994380

Subjects:
Primary: 60E07

Keywords: Symmetric stable laws

Rights: Copyright © 1981 Institute of Mathematical Statistics

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Vol.9 • No. 4 • August, 1981
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