This function calculates the g-value for the harmonic analysis test developed by R.A. Fisher (1929). Harmonic analysis refers to Fast Fourier Transform (FFT) results. Specifically, g is the proportion (squared modulus of one frequency divided by the sum of all squared moduli). In order for g to be statistically significant in the harmonic analysis test, it needs to be at least g-value at significance level \(\alpha\). Please note that for the rth largest frequency, if any of the previous (r-1) frequencies is not significant, then the rth largest frequency is also non-significant.
gharmonic(n, r, p, tol = 10^-7, init = NULL)the total number of frequencies in FFT results.
the modulus of the tested frequency is ranked as the rth largest among all frequencies.
the FFT result of the tested frequency expressed as the squared modulus divided by the sum of the squared moduli by all frequencies (proportion: m_r^2/(m_1^2+...+m_n^2)).
the tolerance level during calculation. The default is 10^-7.
the crude estimate for g-value if known. It is not called to calculate usual g-values.
The g-value calculated by the harmonic test.
Fisher, R. A. (1929). Tests of significance in harmonic analysis. Proceedings of the Royal Society of London. Series A, 125(796), 54-59.
# NOT RUN {
gharmonic(n=100,r=1,p=0.05)
# }
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