Известия Томского политехнического университета: Инжиниринг георесурсов (May 2019)
Modernization of Ord distribution for approximation of the bilateral discrete distributions of experimental data
Abstract
The urgency of considered issue is caused by the need to improve the accuracy and to simplify the approximation of experimental discrete data laws for bilateral distribution. Discrete distribution laws have wide practical application of probabilistic models as signal fluctuations in solving the synthesis of optimal methods for receiving and processing information in optical radar and communications. It is often necessary to use a generalized discrete distribution law, as each of the known laws of distribution alone can not achieve the necessary degree of integration of data with respect to fluctuations of optical signals. The main aim of the study: modernization of the Ord difference equation and getting on basis of its solving the distribution law for generalized two-way discrete random variable, and development of the method for identifying the main types of discrete distribution laws applied in practice. The methods used in the study: calculations using methods of the probability theory and statistics, as well as the software MathCAD; methods of integral and differential calculus. The results: The authors have modernized the Ord difference equation and have received its solution in the form of generalized probability distribution. It was shown that the known discrete distribution laws, such as uniform, binomial, Poisson, negative binomial, hyper-geometric, negative hypergeometricparticular are the particular cases of the obtained distribution. The paper introduces the diagram of the bilateral distribution laws of discrete random variable, which shows the existence areas of the above discrete distribution laws. The authors considered numerical characteristics of the generalized distribution and on its basis developed the method of identifying the main types of discrete distribution laws applied in practice.
