In this chapter, we derive distributional representations for volumes of random parallelotopes spanned by independent random vectors in \(\mathbb {R}^d\) with rotationally invariant distributions. Formulas for the moments of these volumes are also given.

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Volumes of Beta-Type Parallelotopes

  • Zakhar Kabluchko,
  • David Albert Steigenberger,
  • Christoph Thäle

摘要

In this chapter, we derive distributional representations for volumes of random parallelotopes spanned by independent random vectors in \(\mathbb {R}^d\) with rotationally invariant distributions. Formulas for the moments of these volumes are also given.