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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.
We introduce a new statistical and variational approach to the phase estimation algorithm (PEA). Unlike the traditional and iterative PEAs which return only an eigenphase estimate, the proposed method can determine any unknown eigenstate-eigenphase p
We propose a statistical approach to tornadoes modeling for predicting and simulating occurrences of tornadoes and accumulated cost distributions over a time interval. This is achieved by modeling the tornadoes intensity, measured with the Fujita sca
The maximum entropy principle can be used to assign utility values when only partial information is available about the decision makers preferences. In order to obtain such utility values it is necessary to establish an analogy between probability an
The basic idea behind Rayleighs criterion on resolving two incoherent optical point sources is that the overlap between the spatial modes from different sources would reduce the estimation precision for the locations of the sources, dubbed Rayleighs
We present a method to reconstruct the complete statistical mode structure and optical losses of multimode conjugated optical fields using an experimentally measured joint photon-number probability distribution. We demonstrate that this method evalua