The probability density function of a transformation-based hyperellipsoid sampling technique
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- Publication Date
- Abstract
Sun and Farooq showed that random samples can be efficiently drawn from an arbitrary n-dimensional hyperellipsoid by transforming samples drawn randomly from the unit n-ball. They stated that it was a straightforward to show that, given a uniform distribution over the n-ball, the transformation results in a uniform distribution over the hyperellipsoid, but did not present a full proof. This technical note presents such a proof.
- Publication Details
- Type
- Technical Report
- Institution
- Autonomous Space Robotics Lab (ASRL), University of Toronto
- Number
- TR-2014-JDG004
- arXiv Identifier
- 1404.1347 [math.ST]
- Manuscript
- Open-Access PDF
- https://arxiv.org/pdf/1404.1347
- Google Scholar
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- BibTeX Entry
@techreport{gammell_arxiv14b,
author = {Jonathan D Gammell and Timothy D Barfoot},
title = {The probability density function of a transformation-based hyperellipsoid sampling technique},
institution = {Autonomous Space Robotics Lab ({ASRL}), University of Toronto},
year = {2014},
number = {TR-2014-JDG004},
month = apr,
note = {{arXiv}:1404.1347 {[math.ST]}},
}