The Correct Probability Distribution for the Phase Dispersion Minimization Periodogram

Autor:	A. Schwarzenberg-Czerny
Rok vydání:	1997
Předmět:	Physics business.industry Phase dispersion minimization Astronomy and Astrophysics Weighting F-distribution symbols.namesake Optics Space and Planetary Science symbols Probability distribution Sensitivity (control systems) business Beta distribution Algorithm Fourier series Statistic
Zdroj:	The Astrophysical Journal. 489:941-945
ISSN:	1538-4357 0004-637X
DOI:	10.1086/304832
Popis:	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.
Databáze:	OpenAIRE
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