TESTS FOR UNIFORMITY OF A CIRCULAR DISTRIBUTION.

Abstract

Suppose that a sample of size n is drawn from a circular distribution. Arbritrarily establish an origin of the circle and measure distances from this origin in a clockwise direction. Let N(t,x) denote the number of observations on the arc between but not including x, to and including (x+t) and define (A sub n)(t) = (1/n) the integral from zero to one of (N(t,x)-nt)squared dx. Ajne (1968), proposed most powerful test for uniformity invariant under rotation of a circle against certain 'close' alternatives rejects when (A sub n)(1/2) is large. Watson (1967), obtained the asymptotic distribution. This paper extends Watson's result to 0 < t = or < 1/2. (Author)

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1969
Accession Number
AD0699164

Entities

People

  • Edward D. Rothman

Organizations

  • Johns Hopkins University

Tags

DTIC Thesaurus Topics

  • Acquisition
  • Angular Motion
  • Data Acquisition
  • Integrals
  • Mathematics
  • Observation
  • Rotation

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Graph Algorithms and Convex Optimization.
  • Statistical inference.