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Orthogonal Polynomials through Moment Generating Functionals
SIAM Journal on Mathematical Analysis, 1978It is shown that if the linear functional w generates moments $\{ \mu _i \} _{i = 0}^\infty $ through the formula $\mu _i = \langle {w,x^i } \rangle $, $i = 0,1, \cdots $, then the Chebyshev polyno...
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Estimation of the Moment Generating Function
Communications in Statistics - Simulation and Computation, 1989A number of statistical problems use the moment generating function (mgf) for purposes other than determining the moments of a distribution. If the distribution is not completely specified, then the mgf must be estimated from available data. The empirical mgf makes no assumptions concerning the underlying distribution except for the existence of the ...
Edward E. Gbur, Robert A. Collins
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Extremes of Normed Empirical Moment Generating Function Processes
Extremes, 2003Let \(X_i\) be i.i.d. r.v.s with moment generating function \(S(\vartheta)=\mathbf{E}\exp(\vartheta X_i)\), \(\Theta=\{\vartheta: S(\vartheta)
Stewart, Michael, Robinson, John
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Moment Generating Function of Uncertain Variable
2018 10th International Conference on Intelligent Human-Machine Systems and Cybernetics (IHMSC), 2018Within the framework of uncertainty theory, this paper focuses on the moment generating function of an uncertain variable, which is a useful mathematical analytic tool to deal with uncertain variable. Furthermore, as an extension of moment generating function, Laplace transform of any nonnegative uncertain variable is discussed and some results between
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Moment Generating and Free Energy Functionals
2017In this section, we will construct the moment generating function for the Wright–Fisher model and derive a partial differential equation that it satisfies. This differential equation encodes all the moment evolution equation s from the Sect.
Julian Hofrichter +2 more
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The moment generating function has its moments
Journal of Statistical Planning and Inference, 1986For positive random variables all real moments of positive degree are obtained from the moment generating function. In case of moments of negative degree some integrability conditions on the moment generating function are required. Some generalizations and applications are discussed.
Cressie, Noel A, Borkent, M
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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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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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Conditional Moment Generating Functions for Integrals and Stochastic Integrals
SIAM Journal on Control and Optimization, 2002This paper presents two methods for computing filtered estimates for moments of integrals and stochastic integrals of continuous-time nonlinear systems. The first method utilizes recursive stochastic partial differential equations. The second method utilizes conditional moment generating functions. An application of these methods leads to the discovery
Charalambous, Charalambos D. +5 more
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