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We show via both analytical calculation and numerical simulation that the optimal cross-correlation statistic (OS) for stochastic gravitational-wave-background (GWB) searches using data from pulsar timing arrays follows a generalized chi-squared (GX2) distribution-i.e., a linear combination of chi-squared distributions with coefficients given by the eigenvalues of the quadratic form defining the statistic.
1908
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R. W. Hellings and G. S. Downs, “Upper limits on the isotropic gravitational radiation background from pulsar timing analysis,” Astrophys. J. Lett. 265
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Paul B. Demorest, Measuring the gravitational wave background using precision pulsar timing , Ph.D. thesis, University of California, Berkeley (2007)
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Xavier Siemens, Justin Ellis, Fredrick Jenet, and Joseph D Romano, “The stochastic background: scaling laws and time to detection for pulsar timing arrays,” Classical and Quantum Gravity 30
2013
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2015
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2016
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Joseph D. Romano and Neil. J. Cornish, “Detection methods for stochastic gravitational-wave backgrounds: a unified treatment,” Living Reviews in Relativity 20
2017
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Sarah J. Vigeland, Kristina Islo, Stephen R. Taylor, and Justin A. Ellis, “Noise-marginalized optimal statistic: A robust hybrid frequentist-bayesian statistic for the stochastic gravitational-wave background in pulsar timing arrays,” Phys. Rev. D 98
2018
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2020
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2018
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2018
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Jeffrey S. Hazboun, Joseph D. Romano, and Tristan L. Smith, “Realistic sensitivity curves for pulsar timing arrays,” Phys. Rev. D 100
2019
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Jeffrey Hazboun, Joseph Romano, and Tristan Smith, “Hasasia: A Python package for Pulsar Timing Array Sensitivity Curves,” The Journal of Open Source Software 4
2019
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2020
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2020
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2021
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2021
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Abhranil Das and Wilson S Geisler, “A method to integrate and classify normal distributions,” Journal of Vision 21
2021
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2022
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2022
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