### 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 |

State | Published - Apr 1 1997 |

Externally published | Yes |

### Fingerprint

### 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

### Cite this

*Statistics and Probability Letters*,

*32*(4), 367-376.

}

*Statistics and Probability Letters*, vol. 32, no. 4, pp. 367-376.

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Projections on cones, chi-bar squared distributions, and Weyl's formula

AU - Lin, Yong

AU - Lindsay, Bruce G.

PY - 1997/4/1

Y1 - 1997/4/1

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

UR - http://www.scopus.com/inward/record.url?scp=0031116557&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031116557&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031116557

VL - 32

SP - 367

EP - 376

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

IS - 4

ER -