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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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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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A new form of the moment generating function of Weibull distribution
2013 Ninth International Conference on Natural Computation (ICNC), 2013A generic analysis approach referred to as the moment generating function (MGF) method has been introduced for the purpose of simplifying the evaluation of the performance of digital communication over fading channels. Based on the definition of the MGF, the Meijer's G function and the generalized hypergeometric function, a new closed-form expression ...
Xiang Hou +4 more
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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 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 numerical inversion of the moment generating function
1997The main purpose of this thesis is to apply an algorithm for the numerical inversion of the Laplace transform that recovers the probability density function (PDF) of a sum of nonnegative continuous random variables. The Laplace transform is used in many disciplines.
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Asymptotics of the Moment Generating Function for the Range of Random Walks
Journal of Theoretical Probability, 2001The author considers a simple random walk \(\{S_n\}^\infty_{n= 0}\) on the \(d\)-dimensional integer lattice \(\mathbb{Z}^d\); that is, \(S_0= 0\) and \(S_n= X_1+ X_2+\cdots+ X_n\), where the \(X_n\)'s are independent and identically distributed random variables with values in \(\mathbb{Z}^d\), such that \(P[X_1= x]= d/2\) if \(x\in\mathbb{Z}^d\) is a ...
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Moment Generating Function of the Age of Gossip in Networks
2023 57th Asilomar Conference on Signals, Systems, and Computers, 2023Mohamed A. Abd-Elmagid +1 more
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