Approximation an estimate of the ss-distributions stability factor

Authors

DOI:

https://doi.org/10.15587/1729-4061.2014.20245

Keywords:

stable distributions, stability factor estimate, fractional moments, asymptotic variance of estimates

Abstract

The problem of approximating a stability factor estimate of alpha-stable distributions, obtained by the method of fractional moments,has been considered. Such distributions are widely used in models of stochastic processes, describing a wide range of processes and phenomena.

The analysis of existing methods for estimating parameters of stable distributions has been carried out. One of the new and promising methods for solving the problem under consideration is the method of non-integer (fractional) moments.

It has been noted that the formula for calculating the stability factor estimate, developed in accordance with this method, contains a non-elementary and rarely used function (inverse to a gamma function), that significantly complicates using such estimate in applied problems.

The problem of approximating the stability factor estimate has been set and successfully solved in the paper. The original dependence has been approximated with a simple fractional-linear function with quite a sufficient practical accuracy.

The suggested approximation has given an opportunity of adjusting an asymptotic variance estimate of the parameter under estimation regarding its true value. As a result, the discrepancy between a theoretical estimate and the data of numerical experiments has been eliminated.

The conducted numerical modeling has fully justified obtained results.

Author Biography

Вадим Леонидович Шергин, Kharkov National University of Radio Electronics Lenina av., 14, Kharkov, Ukraine, 61166

Candidat of technical science, docent

Department of artificial intelligence

References

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Published

2014-02-12

How to Cite

Шергин, В. Л. (2014). Approximation an estimate of the ss-distributions stability factor. Eastern-European Journal of Enterprise Technologies, 1(4(67), 34–38. https://doi.org/10.15587/1729-4061.2014.20245

Issue

Vol. 1 No. 4(67) (2014): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

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Copyright (c) 2014 Вадим Леонидович Шергин

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