Geodesic
The Set of Basis Functions Generated by Pearson Type IV Distributions and Its Application to Problems of Statistical Data Analysis and Quantum Mechanics
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Noncommutative Analysis and Quantum Information Theory, Tome 324 (2024), pp. 60-72

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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. 
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     author = {Yu. I. Bogdanov and N. A. Bogdanova and V. F. Lukichev},
     title = {The {Set} of {Basis} {Functions} {Generated} by {Pearson} {Type} {IV} {Distributions} and {Its} {Application} to {Problems} of {Statistical} {Data} {Analysis} and {Quantum} {Mechanics}},
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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. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Noncommutative Analysis and Quantum Information Theory, Tome 324 (2024), pp. 60-72. http://geodesic.mathdoc.fr/item/TM_2024_324_a5/