Maximum likelihood algorithm for approximation of local fluctuational fluxes at the plasma periphery by fractional stable distributions

Abstract

Statistical properties of a local fluctuational fluxes measured at the plasma edge are investigated in the work. It's shown that the amplitudes increments of the local fluctuational fluxes decrease by power law. For approximation of experimental PDFs the fractional stable distributions are used. The new algorithm of statistical estimation of the FSD parameters based on maximum likelihood method is described. By using of the algorithm the parameters of FSD are estimated by using experimental samples. It is shown good agreement between experimental and theoretical distributions. On the basis of this results the conclusion is made about applicability of the CTRW model for description of a processes underlying of the plasma turbulence.

Application of the fractional stable distributions for approximation of gene expression profiles

“…There is only two method of estimation of parameters of FSD in present time. The first method has been described Saenko (2012) and estimator is obtained on basis maximum likelihood method. The second method has been described in the work Bening et al (2004) and estimators were obtained on basis the moment method.…”

“…Indeed, it is necessary to know analytical expression for FSD for calculation of likelihood function at usage the first method. In the article Saenko (2012) this difficulty succeeded avoiding by usage of local estimator of Monte Carlo method for calculation of symmetric FSD. However this estimator can be used for estimation of the parameters only of symmetric FSD while gene expression distributions are one-sided distribution.…”