The Hermite polynomials form the basis of a Hilbert space and may be used to get an expansion of the probability density function. Usually, this series is called Gram-Charlier. For practical purposes, only the first few terms of this expansion are taken into consideration. The resulting truncated series may be viewed as the normal probability density function multiplied by a polynomial that acc...

Generalized Diffusion Tensor Imaging (GDTI) [1] is one of the few methods that estimate the ensemble average diffusion propagator from the diffusion weighted signal. It has a statistical approach and views the signal, which under the q-space formalism is the Fourier transform of the propagator, as the characteristic function of the propagator. Instead of taking the inverse Fourier transform of ...

An explicit formula relating the probability density function with its cumulants is derived and discussed. A generalization of the Gram-Charlier expansion is presented, allowing to express one PDF in terms of another. The coefficients of this general expansion are explicitly obtained.

this paper presents a probabilistic confidence-interval based method for optimal placement of shunt capacitors in distribution networks by considering probabilistic characteristics of loads. the main objective function are reducing loss and improving the voltage profile. backward forward sweep method has been employed to obtain the power flow results in distribution system. in addition, integer...

In this paper, we introduce a new approximation for estimating the dynamics of multiserver queues with abandonment. The approximation involves a four-dimensional dynamical system that uses the skewness and kurtosis of the queueing distribution via the Gram Charlier expansion. We show that the additional information captured in the skewness and kurtosis allows us to estimate the dynamics of the ...

In this note we present a series expansion of inverse moments of a non-negative discrete random variate in terms of its factorial cumulants, based on the Poisson-Charlier expansion of a discrete distribution. We apply the general method to the positive binomial distribution and obtain a convergent series for its inverse moments with an error residual that is uniformly bounded on the entire inte...

We propose a new method to efficiently price swap rate derivatives under the LIBOR market model with stochastic volatility and displaced diffusion. This applies series expansion techniques built around Gaussian (Gram–Charlier) or mixture densities polynomial processes. The standard pricing for considered relies on dynamics freezing recover Heston-type which analytical formulas are available. ap...

ABSTRACT. Given a basis for a polynomial ring, the coefficients in the expansion of a product of some of its elements in terms of this basis are called linearization coefficients. These coefficients have combinatorial significance for many classical families of orthogonal polynomials. Starting with a stochastic process and using the stochastic measures machinery introduced by Rota and Wallstrom...

We present a polynomial expansion of the standardized Student-t distribution. Our density, obtained through adjusted method in Bagnato, Potí, and Zoia (2015. “The Role Orthogonal Polynomials Adjusting Hyperbolic Secant Logistic Distributions to Analyse Financial Asset Returns.” Statistical Papers 56 (4): 1205–12340), is an extension Gram–Charlier density Jondeau Rockinger (2001. “Gram-Charlier ...