A powerful test for weak periodic signals with unknown light curve shape in sparse data.

A problem with most tests for periodicity is that they are powerful enough to detect only certain kinds of periodic shapes (or 'light curves') in the case of weak signals. This causes a selection effect with the identification of weak periodic signals. Furthermore, the subjective choice of a test after inspection of the data can cause the identification of false sources. A new test for uniformity called the 'H-test' is derived for which the probability distribution is an exponential function. This test is shown to have a very good power against most light curve shapes encountered in X- and gamma-ray astronomy and therefore makes the detection of sources with a larger variety of shapes possible. The use of the H-test is suggested if no a priori information about the light curve shape is available. It is also shown how the probability distribution of the test statistics changes when a periodicity search is conducted using very small steps in the period or frequency range. The flux sensitivity for various light curve shapes is also derived for a few tests and this flux is on average a minimum for the H-test.