Why the measurement precision of real physical variables is limited

Authors

  • I. I. Gorban головний науковий співробітник Інституту проблем математичних машин і систем НАН України, Київ, Ukraine

Abstract

The research results explaining the restriction causes of measurement precision of real physical variables are presented. It is shown that the imperfect character of the phenomenon of statistical stability that manifests itself in misconvergence (inconsistency) of statistical estimates is a key element in the precision limitation. The peculiarities of the law of average and the central limit theorem of probability theory under conditions of violation of statistical stability are determined. The results of theoretical research are confirmed by experiments. It is drawn to attention that real estimates have hyper-random character. Their hyper-random nature becomes evident when the sample size is large.

Author Biography

I. I. Gorban, головний науковий співробітник Інституту проблем математичних машин і систем НАН України, Київ

Горбань Ігор Ілліч, професор, доктор технічних наук, головний науковий співробітник Інституту проблем математичних машин і систем НАН України, Київ

References

Tikhonov V.I., KHarisov V.N. Statisticheskiy analiz i sintez radiotekhnicheskikh ustroystv i sistem. – M.: Radio i svyaz’, 1991. – 608 s.

Van Tris G. Teoriya obnaruzheniya, otsenok i modulyatsii. – M.: Sovetskoye radio, 1972, T. 1. – 743 s.

Horban' I.I. Teoriya ymovirnostey i matematychna statystyka dlya naukovykh pratsivnykiv ta inzheneriv. – K.: IPMMS NAN Ukrayiny, 2003. – 245 s.

Kolmogorov А.N. Osnovnyye ponyatiya teorii veroyatnostey. – M.: ONTI, 1974. – 120 s.

Gorban’ I.I. Teoriya gipersluchaynykh yavleniy. – K.: NАN Ukrainy, 2007. – 181 s.

Gorban’ I.I. Teoriya gipersluchaynykh yavleniy: fizicheskiye i matematicheskiye osnovy. – K.: Naukova dumka, 2011. – 320 s.

Gorban I.I. Disturbance of statistical stability / In the book "Information Models of Knowledge". Kiev — Sofia: ITHEA, 2010. – P. 410.

Gorban I.I. Disturbance of statistical stability (part II) // Information Theories and Applications. – 2011. – 18, № 4. – P. 321–334.

Gorban I.I. Hyper-random Phenomena: Definition and Description // Information Theories and Applications. – 2008. – 15, № 3. – P. 203–211.

Gorban’ I.I. Narusheniye statisticheskoy ustoychivosti fizicheskikh protsessov // Matematicheskiye mashiny i sistemy. – 2010. – № 1. – S. 171–184.

Gorban’ I.I. Effekt statisticheskoy neustoychivosti v gidrofizike // Trudy desyatoy Vserossiyskoy konferentsii "Prikladnyye tekhnologii gidroakustiki i gidrofiziki". – SPb: Nauka, 2010. – S. 199–201.

Gorban’ I.I. Statisticheskaya ustoychivost’ kolebaniy temperatury vozdukha i osadkov v rayone Moskvy // Matematicheskiye mashiny i sistemy. – 2011. — № 3. – S. 97–104.

Gorban’ I.I., Gorban’ N.I., Novotryasov V.V., YAroshchuk I.O. Issledovaniye statisticheskoy ustoychivosti kolebaniy temperatury shel’fovoy zony okrainnykh morey // Materialy dokladov sed’mogo vserossiyskogo simpoziuma "Fizika geosfer". – Vladivostok: Dal’nauka, 2011. – S. 542– 547.

Gorban’ I.I. Statisticheskaya ustoychivost’ izlucheniya astrofizicheskikh ob"yektov // Matematicheskiye mashiny i sistemy. – 2012. – № 2. – S. 155–160.

Gorban’ I.I. Statisticheski neustoychivyye protsessy: svyaz’ s flikker, neravnovesnymi, fraktal’nymi i tsvetnymi sh·chmami // Izvestiya vuzov. Radioelektronika. – 2012. – 55, № 3. – S. 3–18.

Gorban’ I.I. Kriterii i parametry statisticheskoy neustoychivosti // Matematicheskiye mashiny i sistemy. – 2012. – № 4. – S. 106–114.

Gorban’ I.I. Fenomen statisticheskoy ustoychivosti // ZHurnal tekhnicheskoy fiziki. – 2014. – № 3 – S. 22–30.

Gorban’ I.I. Osobennosti zakona bol’shikh chisel pri narusheniyakh statisticheskoy ustoychivosti // Izvestiya vuzov. Radioelektronika. – 2011. – № 7. – S. 31–42.

Gorban’ I.I. Zakon bol’shikh chisel pri narusheniyakh statisticheskoy ustoychivosti // Matematicheskiye mashiny i sistemy. – 2011. – № 4. – S. 107–115.

Published

2015-12-15

Issue

Section

New methods in system analysis, computer science and theory of decision making