N-sphere chord length distribution

11/20/2014

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by   Panagiotis Sidiropoulos, et al.

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This work studies the chord length distribution, in the case where both ends lie on a N-dimensional hypersphere (N ≥ 2). Actually, after connecting this distribution to the recently estimated surface of a hyperspherical cap SLi11, closed-form expressions of both the probability density function and the cumulative distribution function are straightforwardly extracted, which are followed by a discussion on its basic properties, among which its dependence from the hypersphere dimension. Additionally, the distribution of the dot product of unitary vectors is estimated, a problem that is related to the chord length.