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

Yong Lin, Bruce G. Lindsay

Research output: Contribution to journalArticle

15 Citations (Scopus)

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
StatePublished - Apr 1 1997
Externally publishedYes

Fingerprint

Chi-bar-squared Distribution
Circular cone
Chi-squared distribution
Convex Cone
Unit Sphere
Explicit Formula
Tube
Cone
Projection

All Science Journal Classification (ASJC) codes

  • Statistics, Probability and Uncertainty
  • Statistics and Probability

Cite this

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Projections on cones, chi-bar squared distributions, and Weyl's formula. / Lin, Yong; Lindsay, Bruce G.

In: Statistics and Probability Letters, Vol. 32, No. 4, 01.04.1997, p. 367-376.

Research output: Contribution to journalArticle

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