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Simple random walk statistics. Part I: Discrete time results

Part of: Combinatorial probability Nonparametric inference

Published online by Cambridge University Press:  14 July 2016

W. Katzenbeisser  and
W. Panny
W. Katzenbeisser*
Affiliation:
University of Economics, Vienna
W. Panny*
Affiliation:
University of Economics, Vienna
*
∗Postal address: Department of Statistics, University of Economics, Augasse 2–6, A-1090 Wien, Austria.
∗Postal address: Department of Statistics, University of Economics, Augasse 2–6, A-1090 Wien, Austria.
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Abstract

In a famous paper, Dwass (1967) proposed a method to deal with rank order statistics, which constitutes a unifying framework to derive various distributional results. In the present paper an alternative method is presented, which allows us to extend Dwass's results in several ways, namely arbitrary endpoints, horizontal steps and arbitrary probabilities for the three step types. Regarding these extensions the pertaining rank order statistics are extended as well to simple random walk statistics. This method has proved appropriate to generalize all results given by Dwass. Moreover, these discrete time results can be taken as a starting point to derive the corresponding results for randomized random walks by means of a limiting process.

Keywords

LATTICE PATHSRANK ORDER STATISTICSDWASS'S METHOD

MSC classification

Secondary: 62G30: Order statistics; empirical distribution functions 60C05: Combinatorial probability
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 2 , September 1996 , pp. 311 - 330
Copyright
Copyright © Applied Probability Trust 1996 

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