The generalised Lomb-Scargle periodogram - A new formalism for the floating-mean and Keplerian periodograms

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Table 1:

Probabilities that a periodogram power (P_n, p, P or z) can exceed a given value (P_n,0, p₀, P₀ or z₀) for different normalizations (from Cumming et al. 1999).
Reference level	Range	Probability
population variance	$P_{n}\in[0,\infty)$	${\rm Prob}(P_{n}>P_{n,0})=\exp(-P_{n,0})$
sample variance	$p\in[0,1]$	${\rm Prob}(p>p_{0})=\left(1-p_{0}\right)^{\frac{N-3}{2}}$
- '' -	$P\in[0,\frac{N-1}{2}]$	${\rm Prob}(P>P_{0})=\left(1-\frac{2P}{N-1}\right)^{\frac{N-3}{2}}$
residual variance	$z\in[0,\infty)$	${\rm Prob}(z>z_{0})=\left(1+\frac{2z_{0}}{N-3}\right)^{-\frac{N-3}{2}}$

Source LaTeX | All tables | In the text

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