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arXiv · 1404.1347

The Probability Density Function of a Transformation-based Hyperellipsoid Sampling Technique

Jonathan D. Gammell·Timothy D. Barfoot
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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.

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Jonathan D. Gammell, Timothy D. Barfoot. 2014-04-04. The Probability Density Function of a Transformation-based Hyperellipsoid Sampling Technique. https://arxiv.org/abs/1404.1347

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