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  • 1 All Union Research Institute of Systems Studies 9 Prospekt 60-letiya Oktyabrya 117331 Moscow USSR 9 Prospekt 60-letiya Oktyabrya 117331 Moscow USSR
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Abstract  

A mathematical treatment is given for the family of scientometric laws (usually referred to as the Zipf-Pareto law) that have been described byPrice and do not conform with the usual Gaussian view of empirical distributions. An analysis of the Zipf-Pareto law in relationship with stable non Gaussian distributions. An analysis of the Zipf-Pareto law in relationship with stable non Gaussian distributions reveals, in particular, that the truncated Cauchy distribution asymptotically coincides with Lotka's law, the most well-known frequency form of the Zipf-Pareto law. The mathematical theory of stable non Gaussian distributions, as applied to the analysis of the Zipf-Pareto law, leads to several conclusions on the mechanism of their genesis, the specific methods of processing empirical data, etc. The use of non-Gaussian processes in scientometric models suggests that this approach may result in a general mathematical theory describing the distribution of science related variables.