FITTING THE SUNSPOT CYCLES 10-21 BY A MODIFIED F-DISTRIBUTION DENSITY-FUNCTION

It has been found that sunspot cycles 10-21, represented by quarterly mean values of Zurich sunspot number, can be suitably described by the F-distribution density function provided it is modified by introducing five characteristic parameters, in order to achieve an optimal fitting of each cycle. The average cycle calculated from cycles 10-21 has been used as a basis to forecast time and magnitude of the maximum of each cycle, as a function of various numbers of the first quarterly mean values in the beginning N = 8 to 16 quarters. The standard deviations at a 99% significance level calculated from the observed values depend on N, and vary from 1.6 to 1.1 quarters and 65 to 16 units of sunspot number. A rather sufficient forecast is obtained from N = 12 quarters (with inaccuracy of +/- 1.5 quarters and +/- 24 units); the forecast for cycle 22 yielded, for N = 12, the values t(m) = (15.4 +/- 1.5) quarters (approximately 1990.I) and f(t(m)) = (175 +/- 24 units).