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April, 1973 A Simple Analytic Proof of the Pollaczek-Wendel Identity for Ordered Partial Sums
Jos H. A. De Smit
Ann. Probab. 1(2): 348-351 (April, 1973). DOI: 10.1214/aop/1176996991

Abstract

In this note we prove an identity due to Pollaczek (1952) and Wendel (1960). The identity describes the distributions of ordered partial sums of independent identically distributed random variables and thus generalizes Spitzer's identity. Our proof follows from a simple analytic argument applying a kind of Wiener-Hopf decomposition. We also give an extension of the Pollaczek-Wendel identity.

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Jos H. A. De Smit. "A Simple Analytic Proof of the Pollaczek-Wendel Identity for Ordered Partial Sums." Ann. Probab. 1 (2) 348 - 351, April, 1973. https://doi.org/10.1214/aop/1176996991

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Published: April, 1973
First available in Project Euclid: 19 April 2007

zbMATH: 0277.60040
MathSciNet: MR350864
Digital Object Identifier: 10.1214/aop/1176996991

Rights: Copyright © 1973 Institute of Mathematical Statistics

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Vol.1 • No. 2 • April, 1973
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