Large Deviations Approximations to Distributions of the Total Distance of Compound Random Walks with von Mises Directions

Large Deviations Approximations to Distributions of the Total Distance of Compound Random Walks... This article considers the planar random walk where the direction taken by each consecutive step follows the von Mises distribution and where the number of steps of the random walk is determined by the class of inhomogeneous birth processes. Saddlepoint approximations to the distribution of the total distance covered by the random walk, i.e. of the length of the resultant vector of the individual steps, are proposed. Specific formulae are derived for the inhomogeneous Poisson process and for processes with linear contagion, which are the binomial and the negative binomial processes. A numerical example confirms the high accuracy of the proposed saddlepoint approximations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Methodology and Computing in Applied Probability Springer Journals

Large Deviations Approximations to Distributions of the Total Distance of Compound Random Walks with von Mises Directions

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Publisher
Springer US
Copyright
Copyright © 2016 by Springer Science+Business Media New York
Subject
Statistics; Statistics, general; Life Sciences, general; Electrical Engineering; Economics, general; Business and Management, general
ISSN
1387-5841
eISSN
1573-7713
D.O.I.
10.1007/s11009-016-9523-6
Publisher site
See Article on Publisher Site

Abstract

This article considers the planar random walk where the direction taken by each consecutive step follows the von Mises distribution and where the number of steps of the random walk is determined by the class of inhomogeneous birth processes. Saddlepoint approximations to the distribution of the total distance covered by the random walk, i.e. of the length of the resultant vector of the individual steps, are proposed. Specific formulae are derived for the inhomogeneous Poisson process and for processes with linear contagion, which are the binomial and the negative binomial processes. A numerical example confirms the high accuracy of the proposed saddlepoint approximations.

Journal

Methodology and Computing in Applied ProbabilitySpringer Journals

Published: Oct 12, 2016

References

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