The Rayleigh Statistic in the Case of Weak Signals — Applications and Pitfalls

  • O. C. de Jager
  • B. C. Raubenheimer
  • J. W. H. Swanepoel
Part of the Ettore Majorana International Science Series book series (EMISS, volume 40)


The distribution of the Rayleigh statistic for any kind of light curve is derived. It is shown that a two sigma (Gaussian) hole in an ON-source region with respect to an adjacent OFF-source region is still acceptable after a claimed periodic sinusoidal signal have been subtracted from the ON-source region. This is mainly due to the large effects of Rayleigh fluctuations. It is also shown that most of the present estimators of the signal strength of sinusoidal light curves are conservative in that they underestimate the signal strength if p>1/√n (where n is the number of events). If the signal strength is less than this limit, then one should be careful when interpreting results, since the bias increases rapidly as p→0 which may result in the possibility of identifying a signal where none exists.


Signal Strength Light Curve Pulse Event Very High Energy Small Mean Square Error 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Batschelet, E., 1981., Circular Statistics in Biology, Academic PressMATHGoogle Scholar
  2. Buccheri, R. 1985. (In Proceedings of the Workshop on Techniques in Ultra High Energy Y-ray Astronomy. La Jolla, (USA)) 98–103.Google Scholar
  3. Chadwick, P.M., Dowthwaite, J.C., Harrison, A.B., Kirkman, I.W., McComb, T.J.L., Orford, K.J., and Turver, K.E. 1985a. Nature, 317:236.ADSCrossRefGoogle Scholar
  4. Chadwick, P.M., Dowthwaite, J.C., Harrison, A.B., Kirkman, I.W., McComb, T.J.L., Orford K.J. and Turver, K.E. 1985b., Astron. Astrophys., 151 : L1.ADSGoogle Scholar
  5. Chadwick, P.M., Dipper, N.A., Dowthwaite, J.C., Gibson, A. I., Harrison, A.B., Kirkman, I.W., Lotts, A. P., Mcrae, H.J., McComb, T.J.L., Orford, K.J., Turver, K.E. and Walmsley, M. 1985c., Nature, 318:642.ADSCrossRefGoogle Scholar
  6. Chardin, G. 1986, In Proceedings of the NATO Advanced Research Workshop, Durham (UK). D.Reidel. Dortrecht.Google Scholar
  7. Chardin, G. and Gerbier, G., 1987, Proc. 20th ICRC, Moscow, 1:236.Google Scholar
  8. De Jager, O.C. 1987. Ph.D. Thesis. Unisversity of Potchefstroom.South Africa.Google Scholar
  9. Dowthwaite, J.C., Gibson, A. I., Harrison, A.B., Kirkman, I.W., Lotts, A.P., Mcrae, H.J., Orford, K.J., Turver, K.E., Walmsley, M. 1983. Astron. Astr., 126:1.ADSGoogle Scholar
  10. Gerardi, G., Buccheri, R., Sacco, B. 1982. (In Proceedings of “COMPSTAT 82”,Toulouse (France)), Preprint.Google Scholar
  11. Hart, J.D. 1985, J. Stat. Comp., 21:95.MATHGoogle Scholar
  12. Lamb, R.C. and Weekes, T.C., 1987, Science, 238:1483.CrossRefGoogle Scholar
  13. Lehmann, E.L., 1983, Theory of point estimation. New York: John Wiley and Sons.MATHGoogle Scholar
  14. Li, T-P. and Ma, Y-Q., 1983. Astrophys. J., 272:317.ADSCrossRefGoogle Scholar
  15. Linsley, J., 1975, Proc. 14th ICRC. München., 592.Google Scholar
  16. Mardia, K.V., 1972, Statistics of directional data. New York : Academic Press.MATHGoogle Scholar
  17. Middleditch, J. and Nelson, J., 1976. Astrophys J, 208:567.ADSCrossRefGoogle Scholar
  18. North, A.R., Raubenheimer, B.C., De Jager, O.C., Van Tonder, A.J. and Van Urk, G. 1987, Nature 326(6113) :567.CrossRefGoogle Scholar
  19. Raubenheimer, B.C., North, A.R., De Jager, O.C., Van Urk, G. and Van Tonder, A.J., 1986, Astrophys J, 307 :L43.ADSCrossRefGoogle Scholar
  20. Schou, G., 1978., Biometrika, 65(1):369.MathSciNetMATHGoogle Scholar

Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • O. C. de Jager
    • 1
  • B. C. Raubenheimer
    • 1
  • J. W. H. Swanepoel
    • 2
  1. 1.Dept. of PhysicsPU for CHEPotchefstroomSouth Africa
  2. 2.Dept. of StatisticsPU for CHEPotchefstroomSouth Africa

Personalised recommendations