The Probability Density Function of a Transformation-based Hyperellipsoid Sampling Technique
Abstract
Sun and Farooq [2] 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:
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arXiv e-prints
- Pub Date:
- April 2014
- DOI:
- 10.48550/arXiv.1404.1347
- arXiv:
- arXiv:1404.1347
- Bibcode:
- 2014arXiv1404.1347G
- Keywords:
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- Mathematics - Statistics Theory
- E-Print:
- 4 pages