Mikhail G. Dorrer

Reshetnev Siberian State University of Science and Technology

The paper describes the creation and evaluation of the performance of a neural network model of the probability distribution density function of a random variable, given by a set of measurements of a random variable in the absence of the identification stage of the distribution law. The need to solve this problem is caused by limitations introduced into the accuracy of calculating the probability distribution density function of a random variable both by the tabular-histogram method and in the case of applying approaches to the identification of the distribution law. The problem was solved in Python using the TensorFlow neural network library by creating a neural network model based on the Sequential class with fully connected Dense layers, trained on data from numerical differentiation of the random variable distribution function. The accuracy of the forecast was estimated using the Kullback-Leibler distance measure for various ratios of the volume of experimental data and the number of interpolation intervals on synthetic test data generated for 5 laws of distribution - Rayleigh, Weibull, gamma, exponential and normal (Gaussian). To assess the predictive ability of the approach when testing the interpolator, random variable samples shifted relative to those used in training were used. The proposed solution showed a significantly higher accuracy in calculating the values of the distribution density of a random variable compared to the histogram method. The developed approach will be implemented in the modeling part of the digital twin of a business process based on the mathematical apparatus of stochastic GERT networks.

stochastic models, random variable distribution density, neural networks, digital process models