ASYMPTOTIC THEORY OF A CLASS OF TESTS FOR UNIFORMITY OF A CIRCULAR DISTRIBUTION.
Abstract
Let (x sub 1, x sub 2,..., x sub n) be independent realizations of a random variable taking values on a circle C of unit circumference T sub n = (1/n) the integral from 0 to 1 of the quantity (Summation from j=1 to j=n of f(x + x sub j)-n) squared dx, where f(x) is a probability density on C, f epsilon L sub 2 (0,1), and the addition x +(x sub j) is performed modulo 1. T sub n is used to test whether the observations are uniformly distributed on C. It includes as special cases several other statistics previously proposed for the purpose by Ajne, Rayleigh and Watson. The main results of the paper are the asymptotic distributions of T sub n under fixed alternatives to uniformity and under sequences of local alternatives to uniformity. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1968
- Accession Number
- AD0680451
Entities
People
- R. J. Beran
Organizations
- Johns Hopkins University