The Rayleigh Statistic in the Case of Weak Signals — Applications and Pitfalls
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.
KeywordsSignal Strength Light Curve Pulse Event Very High Energy Small Mean Square Error
Unable to display preview. Download preview PDF.
- Buccheri, R. 1985. (In Proceedings of the Workshop on Techniques in Ultra High Energy Y-ray Astronomy. La Jolla, (USA)) 98–103.Google Scholar
- Chardin, G. 1986, In Proceedings of the NATO Advanced Research Workshop, Durham (UK). D.Reidel. Dortrecht.Google Scholar
- Chardin, G. and Gerbier, G., 1987, Proc. 20th ICRC, Moscow, 1:236.Google Scholar
- De Jager, O.C. 1987. Ph.D. Thesis. Unisversity of Potchefstroom.South Africa.Google Scholar
- Gerardi, G., Buccheri, R., Sacco, B. 1982. (In Proceedings of “COMPSTAT 82”,Toulouse (France)), Preprint.Google Scholar
- Linsley, J., 1975, Proc. 14th ICRC. München., 592.Google Scholar