In this article we propose a new approach to computing of functions with random arguments. Approach based on the idea of dimension reduction by to calculating some integrals and the application of numerical probability analysis. We apply one of the basic concepts of numerical probabilistic analysis as the probabilistic extension to computing a function with random arguments. To implement this technique, a new method based on parallel recursive calculations is proposed. Numerical examples are presented demonstrating the effectiveness of the proposed approach.
The paper considers the new approach to the reconstruction of the probability density function similarly the averaged shifted histogram method. An algorithm is used Richardson's extrapolation for increasing accuracy. We prove the estimates of the accuracy of the probability density function and its second derivative to choose the optimal settings for smoothing the histogram and kernel estimators and to consider the optimal choice problem of the bandwidth parameter. Presented the results of numerical experiments.
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