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

Yong Lin; Bruce G. Lindsay

doi:10.1016/s0167-7152(96)00096-x

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

Yong Lin, Bruce G. Lindsay

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	367-376
Number of pages	10
Journal	Statistics and Probability Letters
Volume	32
Issue number	4
DOIs	https://doi.org/10.1016/s0167-7152(96)00096-x
State	Published - Apr 1 1997
Externally published	Yes

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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10.1016/s0167-7152(96)00096-x

Cite this

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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.",

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AU - Lin, Yong

AU - Lindsay, Bruce G.

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N2 - 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.

AB - 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.

KW - Chi-bar squared distribution

KW - Convex cone

KW - Projection

KW - Tube volume

KW - Weyl's formula

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DO - 10.1016/s0167-7152(96)00096-x

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EP - 376

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 4

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

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