## The Annals of Probability

### A Simple Analytic Proof of the Pollaczek-Wendel Identity for Ordered Partial Sums

Jos H. A. De Smit

#### 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.

#### Article information

Source
Ann. Probab., Volume 1, Number 2 (1973), 348-351.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176996991

Digital Object Identifier
doi:10.1214/aop/1176996991

Mathematical Reviews number (MathSciNet)
MR350864

Zentralblatt MATH identifier
0277.60040

JSTOR