. Analysis of the Ap geomagnetic index. (a) The variation of annual means, <Ap>_{τ = 1 yr}. (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 = 1 day} in bins that are 2 index values in width (N is the number of the total of 31 100 samples in each bin and N_max 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 = 1 yr} to which the mauve line is the 3rd-order polynomial fit.