Filtration of histogram evaluation of probability density based on fuzzy data accessibility to a grouping interval

• Main Authors: A. V. Ausiannikau, V. M. Kozel
• Format: Article
• Language: Russian
• Published: Educational institution «Belarusian State University of Informatics and Radioelectronics» 2021-07-01
• Series: Doklady Belorusskogo gosudarstvennogo universiteta informatiki i radioèlektroniki
• Subjects: probability density; fuzzy membership; weighted histogram estimate; histogram filter
• Online Access: https://doklady.bsuir.by/jour/article/view/3103

The paper proposes a histogram estimate of the probability density based on fuzzy data belonging to a grouping interval. A methodology for constructing a histogram estimate using a histogram smoothing filter is presented. The technique of constructing such a filter is described. The main filter parameter is established – the coefficient of the statistical relationship between the amount of data falling into the grouping interval for a single inclusion function and when approaching to use the membership function. The use of an iterative procedure for a histogram filter allows for a greater “smoothness” of the histogram. The simulation results show the effectiveness of using a histogram filter for different data volumes. At the same time, the choice of the number of grouping intervals for the “correct” recognition of probability density becomes not critical. The histogram filter is a simple tool that can easily be built into any algorithm for constructing histogram estimates.