Root approach for estimation of statistical distributions

TL;DR

This paper demonstrates the use of root density estimators with various polynomial bases for reconstructing statistical distributions from data, with applications in quantum state tomography.

Contribution

It introduces a root approach using Chebyshev-Hermite, Laguerre, Kravchuk, and Charlier polynomials for distribution reconstruction, extending quantum state tomography methods.

Findings

Effective distribution reconstruction demonstrated through numerical modeling.

Applicable to quantum state and process tomography.

Provides a framework for polynomial-based statistical analysis.

Abstract

Application of root density estimator to problems of statistical data analysis is demonstrated. Four sets of basis functions based on Chebyshev-Hermite, Laguerre, Kravchuk and Charlier polynomials are considered. The sets may be used for numerical analysis in problems of reconstructing statistical distributions by experimental data. Based on the root approach to reconstruction of statistical distributions and quantum states, we study a family of statistical distributions in which the probability density is the product of a Gaussian distribution and an even-degree polynomial. Examples of numerical modeling are given. The results of present paper are of interest for the development of tomography of quantum states and processes.