Remarks on the distribution of the sample variance in exponential sampling

Lam, H.K.

doi:10.1080/03610918008812181

Cited by 5 publications

(1 citation statement)

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“…While the χ 2 2 distribution does have a characteristic CV of unity, the measured standard deviation divided by the measured mean is a biased estimator of the CV for two reasons: (1) the standard deviation is biased (as a nonlinear transformation of an unbiased estimator: the variance); and (2) the variance and mean of i.i.d.s are not independent for non-Gaussian underlying p.d.f.s (Geary 1936). Closed forms for the p.d.f.s of variance measured for generic sample sizes drawn from exponential distributions are not known (e.g., Lam 1980). The distributions of measured CVs simulated for nine different sample sizes containing between 4 and 1024 i.i.d.…”

Section: The Coefficient Of Variation (Cv) Metricmentioning

confidence: 99%

Coefficients of variation for detecting solar-like oscillations

Bell

Hekker

Kuszlewicz

2018

Monthly Notices of the Royal Astronomical Society

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Detecting the presence and characteristic scale of a signal is a common problem in data analysis. We develop a fast statistical test of the null hypothesis that a Fourier-like power spectrum is consistent with noise. The null hypothesis is rejected where the local "coefficient of variation" (CV)-the ratio of the standard deviation to the mean-in a power spectrum deviates significantly from expectations for pure noise (CV ≈ 1.0 for a χ 2 2-degrees-of-freedom distribution). This technique is of particular utility for detecting signals in power spectra with frequency-dependent noise backgrounds, as it is only sensitive to features that are sharp relative to the inspected frequency bin width. We develop a CV-based algorithm to quickly detect the presence of solar-like oscillations in photometric power spectra that are dominated by stellar granulation. This approach circumvents the need for background fitting to measure the frequency of maximum solar-like oscillation power, ν max . In this paper, we derive the basic method and demonstrate its ability to detect the pulsational power excesses from the wellstudied APOKASC-2 sample of oscillating red giants observed by Kepler. We recover the cataloged ν max values with an average precision of 2.7% for 99.4% of the stars with 4 years of Kepler photometry. Our method produces false positives for < 1% of dwarf stars with ν max well above the long-cadence Nyquist frequency. The algorithm also flags spectra that exhibit astrophysically interesting signals in addition to single, solar-like oscillation power excesses, which we catalog as part of our characterization of the Kepler light curves of APOKASC-2 targets.

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Section: The Coefficient Of Variation (Cv) Metricmentioning

confidence: 99%