Confidence intervals from the Rayleigh test

Abstract

The Rayleigh test is a simple statistical test used to look for periodicity in unbinned, irregularly sampled data. It is primarily a hypothesis test, but, when a signal is claimed, it may also be used to estimate that signal's strength. We present here an analytical method by which confidence intervals for the signal strength can be obtained from the Rayleigh test. The intervals are based on the observed test statistic and represent a fixed level of confidence that the true flux is within the stated boundaries. An extension of the new method is given to cover the related |$Z^2_2$| test. Both tests are widely used in X-and |$\gamma$|-ray astronomy.