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. Analysis of the Ap geomagnetic index. (a) The variation of annual means, <Ap>τ=1yr. (b) The fraction of time in each year when daily means of Ap exceeds the 95 percentile of the overall distribution, Apo = 38, f[Ap > Apo]. (c) The blue histogram shows the probability distribution function (pdf) of daily Ap means <Ap>τ=1day in bins that are 2 index values in width (N is the number of the total of 31 100 samples in each bin and Nmax is the peak value of N) and the mauve line is the cumulative probability distribution (cdf) from which the 95 percentile Apo is defined. (d) The scatter plot of the 85 annual values of f[Ap > Apo] as a function of <Ap>τ=1yr to which the mauve line is the 3rd-order polynomial fit.

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