Elvira Di Nardo - Academia.edu (original) (raw)

Papers by Elvira Di Nardo

Communications in Statistics - Theory and Methods, 2013

By using a symbolic technique known in the literature as the classical umbral calculus, we charac... more By using a symbolic technique known in the literature as the classical umbral calculus, we characterize two classes of polynomials related to Lévy processes: the Kailath-Segall and the time-space harmonic polynomials. We provide the Kailath-Segall formula in terms of cumulants and we recover simple closed-forms for several families of polynomials with respect to not centered Lévy processes, such as the Hermite polynomials with the Brownian motion, the Poisson-Charlier polynomials with the Poisson processes, the actuarial polynomials with the Gamma processes, the first kind Meixner polynomials with the Pascal processes, the Bernoulli, Euler and Krawtchuk polynomials with suitable random walks.

Applied Mathematics and Computation, 2009

This paper introduces a simple and computationally efficient algorithm for conversion formulae be... more This paper introduces a simple and computationally efficient algorithm for conversion formulae between moments and cumulants. The algorithm provides just one formula for classical, boolean and free cumulants. This is realized by using a suitable polynomial representation of Abel polynomials. The algorithm relies on the classical umbral calculus, a symbolic language introduced by Rota and Taylor in [11], that is particularly suited to be implemented by using software for symbolic computations. Here we give a MAPLE procedure. Comparisons with existing procedures, especially for conversions between moments and free cumulants, as well as examples of applications to some well-known distributions (classical and free) end the paper.

Journal of Statistical Planning and Inference, 2016

In order to tackle parameter estimation of photocounting distributions, polykays of acting intens... more In order to tackle parameter estimation of photocounting distributions, polykays of acting intensities are proposed as a new tool for computing photon statistics. As unbiased estimators of cumulants, polykays are computationally feasible thanks to a symbolic method recently developed in dealing with sequences of moments. This method includes the so-called method of moments for random matrices and results to be particularly suited to deal with convolutions or random summations of random vectors. The overall photocounting effect on a deterministic number of pixels is introduced. A random number of pixels is also considered. The role played by spectral statistics of random matrices is highlighted in approximating the overall photocounting distribution when acting intensities are modeled by a non-central Wishart random matrix. Generalized complete Bell polynomials are used in order to compute joint moments and joint cumulants of multivariate photocounters. Multivariate polykays can be successfully employed in order to approximate the multivariate Poisson-Mandel transform. Open problems are addressed at the end of the paper.

In line with the increasing attention paid to deal with uncertainty in ordinal data models, we pr... more In line with the increasing attention paid to deal with uncertainty in ordinal data models, we propose to combine Fuzzy models with \cub models within questionnaire analysis. In particular, the focus will be on \cub models' uncertainty parameter and its interpretation as a preliminary measure of heterogeneity, by introducing membership, non-membership and uncertainty functions in the more general framework of Intuitionistic Fuzzy Sets. Our proposal is discussed on the basis of the Evaluation of Orientation Services survey collected at University of Naples Federico II.

Statistical Papers, 2021

Within the framework of probability models for overdispersed count data, we propose the generaliz... more Within the framework of probability models for overdispersed count data, we propose the generalized fractional Poisson distribution (gfPd), which is a natural generalization of the fractional Poisson distribution (fPd), and the standard Poisson distribution. We derive some properties of gfPd and more specifically we study moments, limiting behavior and other features of fPd. The skewness suggests that fPd can be left-skewed, right-skewed or symmetric; this makes the model flexible and appealing in practice. We apply the model to real big count data and estimate the model parameters using maximum likelihood. Then, we turn to the very general class of weighted Poisson distributions (WPD’s) to allow both overdispersion and underdispersion. Similarly to Kemp’s generalized hypergeometric probability distribution, which is based on hypergeometric functions, we analyze a class of WPD’s related to a generalization of Mittag–Leffler functions. The proposed class of distributions includes the...

$Research paper thumbnail of A fractional generalization of the dirichlet distribution and related distributions$

Fractional Calculus and Applied Analysis, 2021

This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of t... more This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the n partitions of the interval [0, Wn ] are independent and identically distributed random variables following the generalized Mittag-Leffler distribution. The expected value and variance of the one-dimensional marginal are derived as well as the form of its probability density function. A related generalized Dirichlet distribution is studied that provides a reasonable approximation for some values of the parameters. The relation between this distribution and other generalizations of the Dirichlet distribution is discussed. Monte Carlo simulations of the one-dimensional marginals for both distributions are presented.

Bone marrow transplantation, Jan 12, 2018

Predicting mobilization failure before it starts may enable patient-tailored strategies. Although... more Predicting mobilization failure before it starts may enable patient-tailored strategies. Although consensus criteria for predicted PM (pPM) are available, their predictive performance has never been measured on real data. We retrospectively collected and analyzed 1318 mobilization procedures performed for MM and lymphoma patients in the plerixafor era. In our sample, 180/1318 (13.7%) were PM. The score resulting from published pPM criteria had sufficient performance for predicting PM, as measured by AUC (0.67, 95%CI: 0.63-0.72). We developed a new prediction model from multivariate analysis whose score (pPM-score) resulted in better AUC (0.80, 95%CI: 0.76-0.84, p < 0001). pPM-score included as risk factors: increasing age, diagnosis of NHL, positive bone marrow biopsy or cytopenias before mobilization, previous mobilization failure, priming strategy with G-CSF alone, or without upfront plerixafor. A simplified version of pPM-score was categorized using a cut-off to maximize posit...

We consider a stochastic neuronal model in which the time evolution of the membrane potential is ... more We consider a stochastic neuronal model in which the time evolution of the membrane potential is described by a Wiener process perturbed by random jumps driven by a counting process. We consider the first-crossing-time problem through a constant boundary for such a process, in order to describe the firing activity of the model neuron. We build up a new simulation procedure for the construction of firing densities estimates.

Conference On Computer Aided Systems Theory, 2007

For a class of Gauss-Markov processes the asymptotic behavior of the first passage time (FPT) pro... more For a class of Gauss-Markov processes the asymptotic behavior of the first passage time (FPT) probability density function (pdf) through certain time-varying boundaries is determined. Computational results for Wiener, Ornstein-Uhlenbeck and Brownian bridge processes are considered to show that the FPT pdf through certain large boundaries exhibits for large times an excellent asymptotic approximation.

Advances in Applied Probability, 2001

A new computationally simple, speedy and accurate method is proposed to construct first-passage-t... more A new computationally simple, speedy and accurate method is proposed to construct first-passage-time probability density functions for Gauss–Markov processes through time-dependent boundaries, both for fixed and for random initial states. Some applications to Brownian motion and to the Brownian bridge are then provided together with a comparison with some computational results by Durbin and by Daniels. Various closed-form results are also obtained for classes of boundaries that are intimately related to certain symmetries of the processes considered.

Lecture Notes in Computer Science, 2003

Some analytical and computational methods are outlined, that are suitable to determine the upcros... more Some analytical and computational methods are outlined, that are suitable to determine the upcrossing first passage time probability density for some Gauss-Markov processes that have been used to model the time course of neuron's membrane potential. In such a framework, the neuronal firing probability density is identified with that of the first passage time upcrossing of the considered process through a preassigned threshold function. In order to obtain reliable evaluations of these densities, ad hoc numerical and simulation algorithms are implemented. This work has been performed within a joint cooperation agreement between Japan Science and Technology Corporation (JST) and Università di Napoli Federico II, under partial support by INdAM (GNCS). We thank CINECA for making computational resources available to us.

Lecture Notes in Computer Science, 2001

A parallel algorithm is implemented to simulate sample paths of stationary normal processes posse... more A parallel algorithm is implemented to simulate sample paths of stationary normal processes possessing a Butterworth-type covariance, in order to investigate asymptotic properties of the first passage time probability densities for time-varying boundaries. After a self-contained outline of the simulation procedure, computational results are included to show that for large times and for large boundaries the first passage time probability

We consider the first-crossing-time problem through a constant boundary for a Wiener process pert... more We consider the first-crossing-time problem through a constant boundary for a Wiener process perturbed by random jumps driven by a counting process. On the base of a sample-path analysis of the jump-diffusion process we obtain explicit lower bounds for the first-crossing-time density and for the first-crossing-time distribution function. In the case of the distribution function, the bound is improved by use of processes comparison based on the usual stochastic order. The special case of constant jumps driven by a Poisson process is thoroughly discussed.

Algebraic Combinatorics and Computer Science, 2001

Extending the rigorous presentation of the "classical umbral calculus" [28], the so-called partit... more Extending the rigorous presentation of the "classical umbral calculus" [28], 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.

Natural Computing, 2006

The research work outlined in the present note highlights the essential role played by the simula... more The research work outlined in the present note highlights the essential role played by the simulation procedures implemented by us on CINECA supercomputers to complement the mathematical investigations concerning neuronal activity modeling, carried within our group over the past several years. The ultimate target of our research is the understanding of certain crucial features of the information processing and transmission by single neurons embedded in complex networks. More specifically, here we provide a bird’s eye look of some analytical, numerical and simulation results on the asymptotic behavior of first passage time densities for Gaussian processes, both of a Markov and of a non-Markov type. Significant similarities or diversities between computational and simulated results are pointed out.

Mathematical Methods of Statistics, 2010

and so it does not only involve continuous variables. A very simple closed-form formula for Shepp... more and so it does not only involve continuous variables. A very simple closed-form formula for Sheppard's corrections has been recovered by the classical umbral calculus (see [5]) as well as a more general closed-form formula for discrete parent distributions (see [2]). No attention was paid in the literature to multivariate generalizations of Sheppard's corrections, probably due to the complexity of the resulting formulae (see [1]). Via the umbral calculus, the generalization to the multivariate case turns to be straightforward. All these new formulae are particularly suited to be implemented in MAPLE. The theoretical background of these formulae can be found in Di Nardo E. (2010) (see [3])