The Set of Basis Functions Generated by Pearson Type IV Distributions and Its Application to Problems of Statistical Data Analysis and Quantum Mechanics
Abstract:
Using an example of Pearson type IV distributions, we propose a procedure of completing the classical probability distribution to a quantum state. We obtain a wave function corresponding to Pearson type IV distributions and construct the corresponding set of basis functions. Then we demonstrate how the developed method applies to problems of statistical data analysis and quantum mechanics, and show the efficiency of our approach for the problem of approximating statistical distributions with heavy tails.
Keywords:procedure for completing the classical probability distribution to a quantum state, Pearson type IV distributions, statistical distributions with heavy tails, sets of basis functions, position and momentum representations.
This work was supported by the Ministry of Science and Higher Education of the Russian Federation within the state assignment for the Valiev Institute of Physics and Technology of Russian Academy of Sciences (project no. FFNN-2022-0016).
Citation:
Yu. I. Bogdanov, N. A. Bogdanova, V. F. Lukichev, “The Set of Basis Functions Generated by Pearson Type IV Distributions and Its Application to Problems of Statistical Data Analysis and Quantum Mechanics”, Noncommutative Analysis and Quantum Information Theory, Collected papers. Dedicated to Academician Alexander Semenovich Holevo on the occasion of his 80th birthday, Trudy Mat. Inst. Steklova, 324, Steklov Math. Inst., Moscow, 2024, 60–72; Proc. Steklov Inst. Math., 324 (2024), 53–65
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\by Yu.~I.~Bogdanov, N.~A.~Bogdanova, V.~F.~Lukichev
\paper The Set of Basis Functions Generated by Pearson Type IV Distributions and Its Application to Problems of Statistical Data Analysis and Quantum Mechanics
\inbook Noncommutative Analysis and Quantum Information Theory
\bookinfo Collected papers. Dedicated to Academician Alexander Semenovich Holevo on the occasion of his 80th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2024
\vol 324
\pages 60--72
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4377}
\crossref{https://doi.org/10.4213/tm4377}
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\jour Proc. Steklov Inst. Math.
\yr 2024
\vol 324
\pages 53--65
\crossref{https://doi.org/10.1134/S0081543824010061}
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Citation in format AMSBIB
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