The Correct Probability Distribution for the Phase Dispersion Minimization Periodogram

The phase dispersion minimization (PDM) statistic is a popular method for searching for nonsinusoidal pulsations. The method involves comparison of the PDM value with the Fisher-Snedecor F distribution to assess the significance of pulsations. Later, it was demonstrated that the PDM statistic does not follow the F distribution and that the sensitivity of the method in its original form, based on the F distribution, is poor. In the present paper we demonstrate that the PDM statistic follows a beta distribution, which we designate PDM*. We find that the significance of a given detected pulsation according to the relevant beta distribution is higher than the corresponding significance obtained using the F distribution. In addition, we demonstrate that all methods relying on phase binning and variance estimates related to χ² are equivalent for a given sampling, binning, and weighting pattern. We conclude by observing that with the invention of the high-performance Fourier series method, based on orthogonal projections, the original motivation for the use of phase binning for nonsinusoidal signals has weakened considerably.