Algebra and statistics of the solar wind

Statistical studies of properties of the solar wind and interplanetary magnetic field, based on an extended database for the period 1963–2007 including four solar cycles, show that the Gaussian approximation well suites for some parameters as the probability distribution of their numerical values, while for others the lognormal law is preferred. This paper gives an interpretation of these results as associated with predominance of linear or nonlinear processes in composition and interaction of various disturbances and irregularities propagating and originating in the interior of the Sun and its atmosphere, including the solar corona and the solar wind running away from it. Summation of independent random components of disturbances leads, according to the central limit theorem of the probability theory, to the normal (Gaussian) distributions of quantities proper, while their multiplication leads to the normal distributions of logarithms. Thus, one can discuss the algebra of events and associate observed statistical distinctions with one or another process of formation of irregularities in the solar wind. Among them there are impossible events (having null probability) and reliable events (occurring with 100% probability). For better understanding of the relationship between algebra and statistics of events in the solar wind further investigations are necessary.