Gatto, Riccardo (2017). Saddlepoint approximations to the distribution of the total distance of the multivariate isotropic and von Mises–Fisher random walks. Mathematical methods of statistics, 26(1), pp. 2036. Allerton Press 10.3103/S1066530717010021
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This article considers the random walk over Rp, with p ≥ 2, where the directions taken by the individual steps follow either the isotropic or the vonMises–Fisher distributions. Saddlepoint approximations to the density and to upper tail probabilities of the total distance covered by the random walk, i.e., of the length of the resultant, are derived. The saddlepoint approximations are onedimensional and simple to compute, even though the initial problem is pdimensional. Numerical illustrations of the high accuracy of the proposed approximations are provided.
Item Type: 
Journal Article (Original Article) 

Division/Institute: 
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science 
UniBE Contributor: 
Gatto, Riccardo 
Subjects: 
500 Science > 510 Mathematics 
ISSN: 
10665307 
Publisher: 
Allerton Press 
Language: 
English 
Submitter: 
Lutz Dümbgen 
Date Deposited: 
25 Jul 2017 09:57 
Last Modified: 
01 Feb 2018 02:30 
Publisher DOI: 
10.3103/S1066530717010021 
BORIS DOI: 
10.7892/boris.101484 
URI: 
https://boris.unibe.ch/id/eprint/101484 