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Random Functions with Decomposable in Series Two-dimensional Probality Distributions


V.V. Gubarev

The analytical decision of various theoretical and practical problems demands knowledge of various models of random functions (RF), in particular processes and sequences, as functions of the continuous or discrete argument treated as time. Special interest models of RF with nonlinear function of regression thus have. This results from the fact that application of the traditional correlation-spectral analysis thus or inconveniently, or is essentially impossible. It is necessary to enter their «nonlinear» analogues, for example, concorrelation functions and spectral density, invariant to any monotonous one – to – one transformations of RF and frequently, are easier definable connectional parameters over of two-dimensional probability distributions. In article the class of RF with linear and nonlinear functions of regressions is considered, the two-dimensional probability density distribution of which can be presented decomposition in orthogonal series. Among them such, which weight functions are allocated are equal to one-dimensional probability distributions. Private examples of investigated RF (with two-dimensional distributions Gauss, -Gubarev and its special cases – Nakagamy, Маxwell, Rayleigh, Vaybull-Gnedenko, exponential, gamma; Pearson I, cosinus - phases of normal process, аrcsin.) are considered. For them formulas of communication correlation and concorrelation functions with parameters of two-dimensional distribution are resulted, shown an accessory to RF with linear or nonlinear regressions. The parities defining the general rules of a finding correlation – spectral, concorrelation -spectral and halfconcorrelation - spectral characteristics for considered RF are resulted. In the conclusion the problems which are object to the prime decision are resulted.

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