
Accession Number : AD0680451
Title : ASYMPTOTIC THEORY OF A CLASS OF TESTS FOR UNIFORMITY OF A CIRCULAR DISTRIBUTION.
Descriptive Note : Technical rept.,
Corporate Author : JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF STATISTICS
Personal Author(s) : Beran,R. J.
Report Date : NOV 1968
Pagination or Media Count : 23
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)
Descriptors : (*DISTRIBUTION THEORY, STATISTICAL TESTS), DISTRIBUTION FUNCTIONS, MONTE CARLO METHOD, FOURIER ANALYSIS, INTEGRAL TRANSFORMS, PROBABILITY, SIMULATION, SAMPLING, MATRICES(MATHEMATICS), THEOREMS
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE