Statistical description of non-Gaussian samples in the F2 layer of the ionosphere during heliogeophysical disturbances

Abstract

An adequate statistical method should be developed in order to predict probabilistically the range of ionospheric parameters. This problem is solved in this paper. The time series of the critical frequency of the layer F2−foF2(t) were subjected to statistical processing. For the obtained samples {δfoF2}, statistical distributions and invariants up to the fourth order are calculated. The analysis shows that the distributions differ from the Gaussian law during the disturbances. At levels of sufficiently small probability distributions, there are arbitrarily large deviations from the model of the normal process. Therefore, it is attempted to describe statistical samples {δfoF2} based on the Poisson model. For the studied samples, the exponential characteristic function is selected under the assumption that time series are a superposition of some deterministic and random processes. Using the Fourier transform, the characteristic function is transformed into a nonholomorphic excessive-asymmetric probability-density function. The statistical distributions of the samples {δfoF2} calculated for the disturbed periods are compared with the obtained model distribution function. According to the Kolmogorov’s criterion, the probabilities of the coincidence of a posteriori distributions with the theoretical ones are P ~ 0.7–0.9. The conducted analysis makes it possible to draw a conclusion about the applicability of a model based on the Poisson random process for the statistical description and probabilistic variation estimates during heliogeophysical disturbances of the variations {δfoF2}.