Projections on cones, chi-bar squared distributions, and Weyl's formula

Yong Lin, Bruce G. Lindsay

Research output: Contribution to journalArticle

16 Scopus citations

Abstract

Using Weyl's formula for the volume of the tube about a manifold in the unit sphere, we show that the distribution of the squared length of the projection of the normal variate to any smooth convex cone is a mixture of chi-squared distributions and we give the explicit formulas for the weights. We also give the application of our work to circular cones.

Original languageEnglish (US)
Pages (from-to)367-376
Number of pages10
JournalStatistics and Probability Letters
Volume32
Issue number4
DOIs
StatePublished - Apr 1 1997

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Chi-bar squared distribution
  • Convex cone
  • Projection
  • Tube volume
  • Weyl's formula

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