The Statistical Stability Phenomenon

Authors: Gorban, Igor I.
For the first time the theory of hyper-random phenomena developed by the author is presented in English, in an extensive and coherent way
Broadens our understanding of statistical stability
An original contribution to measurement theory

This monograph investigates violations of statistical stability of physical events, variables, and processes and develops a new physical-mathematical theory taking into consideration such violations – the theory of hyper-random phenomena. There are five parts. The first describes the phenomenon of statistical stability and its features, and develops methods for detecting violations of statistical stability, in particular when data is limited. The second part presents several examples of real processes of different physical nature and demonstrates the violation of statistical stability over broad observation intervals. The third part outlines the mathematical foundations of the theory of hyper-random phenomena, while the fourth develops the foundations of the mathematical analysis of divergent and many-valued functions. The fifth part contains theoretical and experimental studies of statistical laws where there is violation of statistical stability.
The monograph should be of particular interest to engineers and scientists in general who study the phenomenon of statistical stability and use statistical methods for high-precision measurements, prediction, and signal processing over long observation intervals.

Number of Pages
XXXIX, 322
Number of Illustrations and Tables
108 b/w illustrations, 7 illustrations in colour
Additional Information
Originally published by Naukova Dumka Publishing House of National Academy of Sciences of Ukraine, Kiev, 2014
Topics
Appl. Mathematics / Computational Methods of Engineering
Measurement Science, Instrumentation
Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences
Complex Systems
Mathematical Applications in the Physical Sciences
Statistical Physics and Dynamical Systems



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