The article derives a novel Gram-Charlier A (GCA) Series based Extended Rule-of-Thumb (ExROT) for bandwidth selection in Kernel Density Estimation (KDE). There are existing various bandwidth selection rules achieving minimization of the Asymptotic Mean Integrated Square Error (AMISE) between the estimated probability density function (PDF) and the actual PDF. The rules differ in a way to estima...

operations are de ned as upgraded versions of previous ones. This ispossible only because of the systematic use of speci cations, since a correctreuse of previous operations can be based on explicit reasoning. Moreover, themathematical framework used by this version is still weaker than the previousones, since there is no abstract xpoint at all, even in theory. Finally, this ana...

The object of this paper is to prove combinatorially several (13 of them) limit formulas relating different families of hypergeometric orthogonal polynomials in Askey’s chart classifying them. We first find a combinatorial model for Hahn polynomials which, as pointed out by Foata at the ICM (1983), “contains” models for Jacobi, Meixner, Krawtchouk, Laguerre and Charlier polynomials. Seven limit...

Cognitive radio arises to be tempting solution to the spectral congestion problem by introducing opportunistic usage of the frequency bands that are not heavily occupied by licensed users. Spectrum sensing plays a crucial role in the cognitive radio technology to prevent damaging interference to the primary users and to reliably and quickly spot the white spaces in the spectrum and utilize the ...

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This paper is devoted to the analysis of distribution total magnetic quantum number $M$ in a relativistic subshell with $N$ equivalent electrons momentum $j$. analyzed through its cumulants and their generating function, for which an analytical expression provided. function also allows us get values at any order. Such are useful obtain moments various orders. Since distinct subshells additive t...

A notion of t-designs in the symmetric group on n letters was introduced by Godsil 1988. In particular, t-transitive sets permutations form a t-design. We derive upper bounds covering radius these designs, as function and t terms largest zeros Charlier polynomials.