Related papers: Higher Order Moments Generation by Mellin Transfor…
The compound models of clutter statistics are found suitable to describe the nonstationary nature of radar backscattering from high-resolution observations. In this letter, we show that the properties of Mellin transform can be utilized to…
Geometric moments and moment invariants of image artifacts have many uses in computer vision applications, e.g. shape classification or object position and orientation. Higher order moments are of interest to provide additional feature…
First, we present a concise glossary of formulas for composition of standard, cumulant, factorial, and factorial cumulant moments in superposition (compound) models, where final particles are created via independent emission from a…
In this paper, we present methods of obtaining single moments of order statistics arising from posibly dependent and non-identically distributed discrete random variables. We derive exact and approximate formulas convenient for numerical…
We compute Mellin moments of the heavy-quark structure functions in deep-inelastic scattering at next-to-leading order in quantum chromodynamics, retaining their full dependence on the heavy-quark mass. Using the optical theorem and the…
We propose a method to remove the contributions of pileup events from higher-order cumulants and moments of event-by-event particle distributions. Assuming that the pileup events are given by the superposition of two independent…
Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has…
We first provide some properties of the Mellin transform of nonnegative random variables, such that monotonicity, injectivity and effect of size biasing. Convergence of Mellin transforms is also entirely formalized through convergence in…
The description of multiplicity distributions in terms of the ratios of cumulants to factorial moments is analyzed both for data and for the Monte Carlo generated events. For the PYTHIA generated events the moments are investigated for the…
Mixture models are a fundamental tool in applied statistics and machine learning for treating data taken from multiple subpopulations. The current practice for estimating the parameters of such models relies on local search heuristics…
Moment methods to reconstruct images from their Radon transforms are both natural and useful. They can be used to suppress noise or other spurious effects and can lead to highly efficient reconstructions from relatively few projections. We…
We propose a high-order stochastic-statistical moment closure model for efficient ensemble prediction of leading-order statistical moments and probability density functions in multiscale complex turbulent systems. The statistical moment…
The purpose of the present paper is to establish moment estimates of Rosenthal type for a rather general class of random variables satisfying certain bounds on the cumulants. We consider sequences of random variables which satisfy a central…
Scattering moments provide nonparametric models of random processes with stationary increments. They are expected values of random variables computed with a nonexpansive operator, obtained by iteratively applying wavelet transforms and…
Interaction of intense laser beam with an inversion symmetric third order nonlinear medium is modeled as a quartic anharmonic oscillator. A first order operator solution of the model Hamiltonian is used to study the possibilities of…
A new method is presented to determine the gluon density in the proton from jet production in deeply inelastic scattering. By using the technique of Mellin transforms not only for the solution of the scale evolution equation of the parton…
In this paper, we address the problem of classifying clutter returns in order to partition them into statistically homogeneous subsets. The classification procedure relies on a model for the observables including latent variables that is…
Robust tracking of a target in a clutter environment is an important and challenging task. In recent years, the nearest neighbor methods and probabilistic data association filters were proposed. However, the performance of these methods…
Many models such as Long Short Term Memory (LSTMs), Gated Recurrent Units (GRUs) and transformers have been developed to classify time series data with the assumption that events in a sequence are ordered. On the other hand, fewer models…
It is often of interest to perform clustering on longitudinal data, yet it is difficult to formulate an intuitive model for which estimation is computationally feasible. We propose a model-based clustering method for clustering objects that…