## The Annals of Statistics

### Characterization of Type from Maximal Invariant Spectra

Christopher G. Small

#### Abstract

The affine type of distributions on the real line are represented as sequences of distributions of maximal invariants on spheres. It is shown that such a representation characterizes the affine type. A consistency condition is introduced, and it is shown that any sequence of maximal invariant distributions satisfying the condition is generated by some affine type on $\mathbf{R}$.

#### Article information

Source
Ann. Statist., Volume 11, Number 3 (1983), 979-983.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176346263

Digital Object Identifier
doi:10.1214/aos/1176346263

Mathematical Reviews number (MathSciNet)
MR707947

Zentralblatt MATH identifier
0519.62001

JSTOR