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A statistical primer on classical period-finding techniques in astronomy.

Naomi Giertych1, Ahmed Shaban2, Pragya Haravu1

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Summary
This summary is machine-generated.

This study statistically analyzes period-finding methods like phase-dispersion minimization (PDM) and Lomb-Scargle (LS). The analysis of variance (AOV) statistic shows the most power for detecting periodic signals in astronomical data.

Keywords:
astrostatisticsirregularly-spaced time seriesperiod detection

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Area of Science:

  • Astronomy
  • Statistics
  • Data Analysis

Background:

  • Period-finding statistics are crucial for analyzing time-series data, particularly in astronomy.
  • Classical methods include phase-dispersion minimization (PDM), analysis of variance (AOV), string-length (SL), and Lomb-Scargle (LS).
  • Understanding the statistical properties of these methods is essential for accurate period estimation and false alarm probability (FAP) determination.

Purpose of the Study:

  • To investigate the statistical properties of PDM, AOV, SL, and LS power statistics from a statistician's viewpoint.
  • To verify theoretical distributions of these statistics under the null hypothesis and for extreme values.
  • To assess the robustness and detection power of these methods, especially in the context of astronomical time-series data.

Main Methods:

  • Theoretical statistical analysis of PDM, AOV, SL, and LS statistics.
  • Monte Carlo simulations to verify theoretical distributions and assess extreme value behavior.
  • Simulations of data mimicking binary systems and instrument degradation to test robustness and detection power.

Main Results:

  • Scaled PDM follows a beta distribution, AOV follows an F distribution, and LS follows a chi-squared distribution under the null hypothesis.
  • SL statistic lacks a closed-form distribution; extreme values of all statistics follow different distributions than single-period derivations.
  • All tested methods are robust to heteroscedastic noise; AOV demonstrates the highest power for detecting periodic signals in simulated binary systems.

Conclusions:

  • Multiple-testing considerations are vital for accurate FAP bounds, though some methods incorporate these controls.
  • The analysis of variance (AOV) statistic is the most powerful method for detecting periodic signals in astronomical time-series data, aligning with practical observations.
  • The statistical properties of these period-finding methods are well-defined, but their application requires careful consideration of multiple-testing and data characteristics.