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On Minimal-Moment Generating Functions
Extremes, 2002For a distribution function \(F\) on \(R_+\) a minimal-moment generation function is defined as \(\varphi(z)=\sum_{k\geq 1}z^{k-1}m_k\), where \(m_k=\mathbf{E}[\min_{1\leq j\leq k} X_j]\), \(X_j\) are i.i.d. with d.f. \(F\). It is shown that under mild conditions \[ F^{-1}\left(1-{1\over \omega+\varepsilon}\right)- F^{-1}\left(1-{1\over \omega ...
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On a test of normality based on the empirical moment generating function
, 2016We provide the lacking theory for a test of normality based on a weighted $$L^2$$ L 2 -statistic that employs the empirical moment generating function.
N. Henze, Stefan Koch
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Generalized Moment Functions and Orbit Spaces
American Journal of Mathematics, 1987Let X be a complete normal algebraic variety over an algebraically closed field, with an action of a reductive group G. Let \(T\subset G\) be a maximal torus, and let \(X^ T=X_ 1\cup...\cup X_ r\) be the decomposition into connected components of \(X^ T\). The aim of the paper under review is to define a generalized moment function \(f: \{X_ 1,...,X_ r\
Białynicki-Birula, Andrzej +1 more
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Generalized Moments of Additive Functions. II
Lithuanian Mathematical Journal, 2001[Part I, cf. J. Number Theory 32, 281-288 (1989; Zbl 0678.10038).] The first moment inequality valid for every additive function, the celebrated Turán-Kubilius inequality, can be stated as ``the variance of an additive function on the first \(x\) integers is less than a constant times the variance of a sum of naturally defined random variables''.
Indlekofer, K.-H., Kátai, I.
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Moment Generating Functions and Central Moments
2018This section deals with the moment generating functions (m.g.f.) up to sixth order of some discretely defined operators. We mention the m.g.f. and express them in expanded form to obtain moments, which are important in the theory of approximation relevant to problems of convergence.
Vijay Gupta +3 more
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On convergence of moment generating functions
Statistics & Probability Letters, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ushakov, N. G., Ushakov, V. G.
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A Note on the Moment Generating Function
The American Statistician, 1983Abstract A simple proof is given to show that there always exists a neighborhood of zero in which a moment generating function has a power series expansion. Thus, the relation between moments and derivatives of the moment generating function at zero can be obtained without resorting to postcalculus theorems.
S. N.U.A. Kirmani, E. Mirhakkak Esfahani
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Laguerre moments and generalized functions
Journal of Physics A: Mathematical and General, 2002In the paper the link between the moments of the Laguerre polynomials or Laguerre moments and the generalized functions (as the Dirac delta-function and its derivatives) is explored. Several interesting relations are presented. A useful application is related to a procedure for calculating mean values in quantum optics making use of the so-called quasi-
Mizrahi, S. S., Galetti, D.
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Moment generating functions of generalized fading distributions and applications
IEEE Communications Letters, 2008This letter provides novel expressions for the moment generating functions of generalized fading distributions, namely eta-mu and kappa-mu. Our results find applicability in the derivation of several performance metrics, such as average error rate (AER), of a broad class of modulation formats.
Daniel Benevides da Costa +3 more
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