Open AccessMethods of Estimating the Form of the Probability Distribution Density in Tasks of Processing Measurement Results
Author(s) -
V. M. Artyushenko,
В. И. Воловач
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2096/1/012136
Subject(s) - mathematics , probability distribution , probability density function , skewness , kernel density estimation , statistics , multiplicative function , kurtosis , histogram , symmetric probability distribution , principle of maximum entropy , k distribution , estimator , mathematical analysis , computer science , artificial intelligence , image (mathematics)
Issues associated with methods for estimating the shape of the probability distribution density curve are analyzed in order to classify them when processing measurement results. For example, such nonparametric methods as the method of histograms and frequency polygon, as well as the method of classification of distributions, are considered. It is shown that the values of the anticurtosis and entropy coefficient can be taken as independent features of the form of symmetric distributions. For probability distribution densities that have a one-sided character, such as multiplicative noise, a skewness coefficient should be added to the parameters to consider. Recurrent procedures for obtaining current estimates of numerical characteristics of analyzed random processes are given. The results of processing a random process based on recurrent procedures are presented. It is shown that when the number of samples increases, the estimates obtained by using recurrent and non-recurrent procedures converge. The scattering of estimates of probability distribution density parameters, such as variance, relative mean square error, and entropy error, is determined.