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The Statistical Stability Phenomenon

Part of the Mathematical Engineering Book Series

DOI: 10.1007/978-3-319-43585-5

ISBN: 978-3-319-43584-8

Publisher: Springer International Publishing - Springer Journals

Oct 18, 2016

1 - 10 of 21 Chapters

LitStream

The Phenomenon of Statistical Stability and Its Properties

Gorban, Igor I.

Pages: 3 –22

[Here we examine the main manifestations of the phenomenon of statistical stability: the statistical stability of the relative frequency and sample average. Attention is drawn to an emergent property of the phenomenon of statistical stability. We discuss the hypothesis of perfect (absolute or...
LitStream

Determinism and Uncertainty

Gorban, Igor I.

Pages: 23 –43

[Various conceptual views of the structure of the world are examined from the standpoint of determinism and uncertainty. A classification of uncertainties is presented. To present the different types of models, a uniform method using the distribution function is described. A classification of...
LitStream

Formalization of the Statistical Stability Concept

Gorban, Igor I.

Pages: 45 –54

[The notion of statistical stability is formalized and the parameters of statistical instability are introduced. Measurement units are proposed for the statistical instability parameters. We introduce the concepts of statistical stability/instability of processes in both narrow and broad senses...
LitStream

Dependence of the Statistical Stability of a Stochastic Process on Its Spectrum-Correlation Characteristics

Gorban, Igor I.

Pages: 55 –74

[The Wiener–Khinchin transformation is examined. It is noted that there are stochastic processes which do not simultaneously have a correlation function that is typical for a stationary process, and a power spectral density. We determine the dependence of the statistical stability on the power...
LitStream

Experimental Investigation of the Statistical Stability of Physical Processes Over Long Observation Intervals

Gorban, Igor I.

Pages: 77 –90

[Here we discuss experimental studies of the statistical stability of various physical processes. These include the city mains voltage, the height and period of sea waves, variations in the Earth’s magnetic field, currency fluctuations, and variations in the temperature and speed of sound in the...
LitStream

Experimental Investigation of the Statistical Stability of Meteorological Data

Gorban, Igor I.

Pages: 91 –102

[We present experimental studies of the statistical stability of air temperature and precipitation in the Moscow and Kiev areas, and also the wind speed in Chernobyl. It is shown that all these processes are statistically unstable, but that the degree of instability is different in each case. For...
LitStream

Experimental Studies of the Statistical Stability of Radiation from Astrophysical Objects

Gorban, Igor I.

Pages: 103 –109

[Here we discuss experimental studies over long observation intervals (13 years) of the statistical stability of X-ray radiation from three astrophysical objects. It is found that all the studied radiation intensities are statistically unstable. The most stable oscillations are from the pulsar...
LitStream

Statistical Stability of Different Types of Noise and Process

Gorban, Igor I.

Pages: 111 –118

[Different types of noise are studied, in particular, the color noises, flicker noise, and self-similar (fractal) noise. The results of studies of statistical stability of various noises and processes are generalized and the causes of statistical stability violation are investigated. It is found...
LitStream

Hyper-random Events and Variables

Gorban, Igor I.

Pages: 121 –142

[The notion of a hyper-random event is introduced. To describe such events, conditional probabilities and probability bounds are used. The properties of these parameters are presented. The concept of a scalar hyper-random variable is introduced. Here we use conditional distribution functions...
LitStream

Hyper-random Functions

Gorban, Igor I.

Pages: 143 –158

[The notion of a hyper-random scalar function is introduced. Various ways of presenting it are examined, including those based on conditional distribution functions (which provide the most complete characterization of hyper-random functions), the bounds of the distribution function, the...

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