arXiv subjects

E. Di Nardo

Publications and source records attributed to E. Di Nardo.

25 records · Page 2Linked to original sources

arXiv2008

A new method for fast computing unbiased estimators of cumulants

We propose new algorithms for generating $k$-statistics, multivariate $k$-statistics, polykays and multivariate polykays. The resulting computational times are very fast compared with procedures existing in the literature. Such speeding up is obtained by means of a symbolic method arising from the classical umbral calculus. The classical umbral calculus is a light syntax that involves only elementary rules to managing sequences of numbers or polynomials. The cornerstone of the procedures here introduced is the connection between cumulants of a random variable and a suitable compound Poisson random variable. Such a connection holds also for multivariate random variables.

math.ST↗

arXiv2008

Symbolic computation of moments of sampling distributions

By means of the notion of umbrae indexed by multisets, a general method to express estimators and their products in terms of power sums is derived. A connection between the notion of multiset and integer partition leads immediately to a way to speed up the procedures. Comparisons of computational times with known procedures show how this approach turns out to be more efficient in eliminating much unnecessary computation.

stat.CO↗

arXiv2005

A symbolic method for k-statistics

Trough the classical umbral calculus, we provide new, compact and easy to handle expressions of k-statistics, and more in general of U-statistics. In addition such a symbolic method can be naturally extended to multivariate case and to generalized k-statistics.

math.CO↗

arXiv2004

An umbral setting for cumulants and factorial moments

We provide an algebraic setting for cumulants and factorial moments through the classical umbral calculus. Main tools are the compositional inverse of the unity umbra, connected with the logarithmic power series, and a new umbra here introduced, the singleton umbra. Various formulae are given expressing cumulants, factorial moments and central moments by umbral functions.

math.PR↗

arXiv2004

Umbral nature of the Poisson random variables

Extending the rigorous presentation of the classical umbral calculus given by Rota and Taylor in 1994, the so-called partition polynomials are interpreted with the aim to point out the umbral nature of the Poisson random variables. Among the new umbrae introduced, the main tool is the partition umbra that leads also to a simple expression of the functional composition of the exponential power series. Moreover a new short proof of the Lagrange inversion formula is given.

math.PR↗

arXiv2003

On the asymptotic behavior of first passage time densities for stationary Gaussian processes

Making use of a Rice-like series expansion, for a class of stationary Gaussian processes the asymptotic behavior of the first passage time probability density function through certain time-varying boundaries, including periodic boundaries, is determined. Sufficient conditions are then given such that the density asymptotically exhibits an exponential behavior when the boundary is either asymptotically constant or asymptotically periodic.

math.PR↗

arXiv2003

Towards the Modeling of Neuronal Firing by Gaussian Processes

This paper focuses on the outline of some computational methods for the approximate solution of the integral equations for the neuronal firing probability density and an algorithm for the generation of sample-paths in order to construct histograms estimating the firing densities. Our results originate from the study of non-Markov stationary Gaussian neuronal models with the aim to determine the neuron's firing probability density function. A parallel algorithm has been implemented in order to simulate large numbers of sample paths of Gaussian processes characterized by damped oscillatory covariances in the presence of time dependent boundaries. The analysis based on the simulation procedure provides an alternative research tool when closed-form results or analytic evaluation of the neuronal firing densities are not available.

math.PR↗