The Correct Probability Distribution for the Phase Dispersion Minimization Periodogram

Details The Correct Probability Distribution for the Phase Dispersion Minimization Periodogram The Correct Probability Distribution for the Phase Dispersion Minimization Periodogram

Nov 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997apj...489..941s&link_type=abstract

Astrophysical Journal v.489, p.941

Astronomy and Astrophysics

Astronomy

31

Stars: Binaries: Eclipsing, Methods: Data Analysis, Methods: Statistical, Stars: Pulsars: General, Stars: Oscillations, X-Rays: Stars

Scientific paper

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 chi 2 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.

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