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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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On numerical inversion of the moment generating function [PDF]
, 1997 The 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.
Tsang, Andy M
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Testing Skew Normality via the Moment Generating Function
Mathematical Methods of Statistics, 2010 In this paper, goodness-of-fit tests are constructed for the skew normal law. The proposed tests utilize the fact that the moment generating function of the skew normal variable satisfies a simple differential equation.
Meintanis, S.G.
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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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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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Moment-generating function zeros in the study of phase transitions
Physical Review E, 2021Partition function zeros play a central role in the study of phase transitions. Recently, energy probability distribution (EPD) zeros were proposed as an alternative approach that solves some of the implementation issues present in the Fisher zeros method by allowing drastic reduction of the polynomial.
R. G. M. Rodrigues +2 more
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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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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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