  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.

Quantum Physics;Data Analysis, Statistics and Probability