In this article are considered the results of comparative analysis of Rosenblatt-Parzen approximation (ARP) and structural risk minimization (SRM) for approximation of probability density of random variables with a bounded scattering region problem. Two approaches to this problem are known: parametric and non-parametric. In accordance to the first approach based on a priori information choose the type of random variable distribution function (DF), which depends on set of parameters, and measure of proximity between theoretical and experimental distribution functions. Non-parametric statistics is based on the approach that allows getting adaptive assessments of empirical DF as some functionalities which do not depend on chosen type of DF based on a priori information. The method density distribution recovery of experimental sample in ARP is based on an assumption that DF is assessed locally in each point using elements of training set from some area of this point. And in this general DF is some linear combination of known nuclear functions. The assessment of density distribution (DD) in SRM method is counted as a type of decomposition using system of trigonometrical functions. The random variables with one- two- and three-modules probability density were used for comparative analysis. The value of integrated error was used for assessment of approximation quality of analysed methods. The assessments of approximation accuracy and calculation time of DD were found via both methods. Summary tables of approximation accuracy and calculation time of DD were created for analysis. It was formulated conclusions about benefits and disadvantages of each method. It was suggested some recommendations for using this or those methods depending on size of source sample.
|Translated title of the contribution||Comparative analysis of Rosenblatt-Parzen method and structural risk minimization method for approximation of the probability density functions of random variables|
|Journal||Cloud of Science|
|Publication status||Published - 2019|
Level of Research Output
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