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We introduce and study a fractional version of the Skellam process of order k by time-changing it with an independent inverse stable subordinator. We call it the fractional Skellam process of order k (FSPoK). An integral representation for its one-dimensional distributions and their governing system of fractional differential equations are obtained. We derive the probability generating function, mean, variance and covariance of FSPoK which are utilized to establish its long-range dependence property. Later, we consider two time-changed versions of the FSPoK. These are obtained by time-changing the FSPoK by an independent Lévy subordinator and its inverse. Some distributional properties and particular cases are discussed for these time-changed processes. [ABSTRACT FROM AUTHOR]

Passes are undoubtedly the more frequent events in football and other team sports. Passing networks and their structural features can be useful to evaluate the style of play in terms of passing behavior, analyzing and quantifying interactions among players. The present paper aims to show how information retrieved from passing networks can have a relevant impact on predicting the match outcome. In particular, we focus on modeling both the scored goals by two competing teams and the goal difference between them. With this purpose, we fit these outcomes using Bayesian hierarchical models, including both in-match and network-based covariates to cover many aspects of the offensive actions on the pitch. Furthermore, we review and compare different approaches to include covariates in modeling football outcomes. The presented methodology is applied to a real dataset containing information on 125 matches of the 2016–2017 UEFA Champions League, involving 32 among the best European teams. From our results, shots on target, corners, and such passing network indicators are the main determinants of the considered football outcomes. [ABSTRACT FROM AUTHOR]

In this article, we establish a L 1 estimate for solutions to Poisson equation with mixed boundary condition, on complete noncompact manifolds with nonnegative Ricci curvature and compact manifolds with positive Ricci curvature respectively. On Riemann surfaces we obtain a Talenti-type comparison. Our results generalize main theorems in Alvino et al. (J Math Pures Appl 9(152):251–261, 2021) to Riemannian setting, and Chen–Li's result (Talenti's comparison theorem for poisson equation and applications on Riemannian manifold with nonnegative Ricci curvature, 2021. arXiv:2104.05568) to the case of variable Robin parameter. [ABSTRACT FROM AUTHOR]

This study introduces three new bivariate distributions on Z2 with a discussion of the main properties of these distributions. The correlation in these distributions varies in range; some have a full range while others can take only positive or negative values. The development of these distributions depends on a trivariate reduction and the extension of the Moran results. Two real applications—the difference in the number of casualties to the number of employees on duty on railroads and the difference in the number of goals scored in the English Premier League in different years—are fitted to the proposed bivariate distributions. [ABSTRACT FROM AUTHOR]

This study introduces three new bivariate distributions on Z2 with a discussion of the main properties of these distributions. The correlation in these distributions varies in range; some have a full range while others can take only positive or negative values. The development of these distributions depends on a trivariate reduction and the extension of the Moran results. Two real applications—the difference in the number of casualties to the number of employees on duty on railroads and the difference in the number of goals scored in the English Premier League in different years—are fitted to the proposed bivariate distributions. [ABSTRACT FROM AUTHOR]

We develop a novel observation-driven model for high-frequency prices. We account for irregularly spaced observations, simultaneous transactions, discreteness of prices, and market microstructure noise. The relation between trade durations and price volatility, as well as intraday patterns of trade durations and price volatility, is captured using smoothing splines. The dynamic model is based on the zero-inflated Skellam distribution with time-varying volatility in a score-driven framework. Market microstructure noise is filtered by including a moving average component. The model is estimated by the maximum likelihood method. In an empirical study of the IBM stock, we demonstrate that the model provides a good fit to the data. Besides modeling intraday volatility, it can also be used to measure daily realized volatility. [ABSTRACT FROM AUTHOR]

In this paper is presented the zero-modified poisson difference and present possible applications of them in the analysis of paired count data. The estimation and inferences of the model parameters were made considering a Bayesian approach using the algorithm of Hamiltonian Markov chain Monte Carlo methods to simulate samples of the joint posterior distribution of interest. Two applications were made for the analysis of paired count data. [ABSTRACT FROM AUTHOR]

In capture-mark-reencounter studies, Pollock’s robust design combines methods for open populations with methods for closed populations. Open population features of the robust design allow for estimation of rates of death or permanent emigration, and closed population features enhance estimation of population sizes. We describe a similar design, but for use with removal data. Data collection occurs on secondary sampling occasions clustered within primary sampling periods. Primary sampling periods are intervals of brief enough duration that it can be safely assumed that the population is unchanged by births, deaths, immigration or emigration during them; all population change and movement occurs between primary sampling periods. Our model provides a basis for inference about population size, changes in population size, and movement rates among sample locations between primary sampling periods. Movement rates are modeled as functions of distance and time. Capture probabilities are modeled as a function of effort. We apply the model to data obtained in attempting to eradicate an introduced population of veiled chameleons (Chamaeleo calyptratus) on the island of Maui in Hawaii.Supplementary materials accompanying this paper appear online. [ABSTRACT FROM AUTHOR]

This study analyses the key factors that shape inter-governorates migration in Tunisia, focusing mainly on the role of demographic, geographical and socio-economic factors in driving migration flows. It uses basic and extended gravity models, as well as Poisson pseudo-maximum-likelihood model for modeling migration data to assess the relative importance of distance, job market characteristics and economic variables. The main findings reveal that inter-governorate migrations in Tunisia are affected by high population size at the origin and destination locations, high unemployment rate at the origin and low unemployment rate at the destination. The results suggest also that migration flows are negatively affected by high job vacancies and the annual average per capita household expenditure at the origin. [ABSTRACT FROM AUTHOR]

In this note, it is shown that the integrated likelihood for the Royle-Nichols model with a Poisson mixing distribution can be expressed as a finite rather than an infinite sum of terms. The advantages which so accrue are discussed and explored by means of two examples. The finite sum formulation of the likelihood is also shown to hold for negative binomial and zero-inflated mixing distributions. Results based on these two mixing distributions proved disappointing however and their use is not recommended unless extensive data are available. [ABSTRACT FROM AUTHOR]

We consider a network model where small base stations (SBSs) have caching capabilities as a means to alleviate the backhaul load and satisfy users' demand. The SBSs are stochastically distributed over the plane according to a Poisson point process (PPP) and serve their users either (i) by bringing the content from the Internet through a finite rate backhaul or (ii) by serving them from the local caches. We derive closed-form expressions for the outage probability and the average delivery rate as a function of the signal-to-interference-plus-noise ratio (SINR), SBS density, target file bitrate, storage size, file length, and file popularity. We then analyze the impact of key operating parameters on the system performance. It is shown that a certain outage probability can be achieved either by increasing the number of base stations or the total storage size. Our results and analysis provide key insights into the deployment of cache-enabled small cell networks (SCNs), which are seen as a promising solution for future heterogeneous cellular networks. [ABSTRACT FROM AUTHOR]

Purpose: Fluoroscopy is an invaluable tool in various medical practices such as catheterization or image-guided surgery. Patient's screen for prolonged time requires substantial reduction in X-ray exposure: The limited number of photons generates relevant quantum noise. Denoising is essential to enhance fluoroscopic image quality and can be considerably improved by considering the peculiar noise characteristics. This study presents analytical models of fluoroscopic noise to express the variance of noise as a function of gray level, a practical method to estimate the parameters of the models and a possible application to improve the performance of noise filtering. Methods: Quantum noise is modeled as a Poisson distribution and results strongly signal-dependent. However, fluoroscopic devices generally apply gray-level transformations (i.e., logarithmic-mapping, gamma-correction) for image enhancement. The resulting statistical transformations of the noise were analytically derived. In addition, a characterization of the statistics of noise for fluoroscopic image differences was offered by resorting to Skellam distribution. Real fluoroscopic sequences of a simple step-phantom were acquired by a conventional fluoroscopic device and were utilized as actual noise measurements to compare with. An adaptive spatio-temporal filter based on the local conditional average of similar pixels has been proposed. The gray-level differences between the local pixel and the neighboring pixels have been assumed as measure of similarity. Filter performance was evaluated by using real fluoroscopic images of a step phantom and acquired during a pacemaker implantation. Results: The comparison between experimental data and the analytical derivation of the relationship between noise variance and mean pixel intensity (noise-parameter models) were presented relatively to raw-images, after applying logarithmic-mapping or gamma-correction and for difference images. Results have confirmed a great agreement (adjusted R-squared values > 0.8). Clipping effects of real sensors were also addressed. A fine image restoration has been obtained by using a conditioned spatio-temporal average filter based on the noise statistics previously estimated. Discussion: Fluoroscopic noise modeling is useful to design effective procedures for noise estimation and image filtering. In particular, filter performance analysis has showed that the knowledge of the noise model and the accurate estimate of noise characteristics can significantly improve the image restoration, especially for edge preserving. Fluoroscopic image enhancement can support further X-ray exposure reduction, medical image analysis and automated object identification (i.e., surgery tools, anatomical structures). [ABSTRACT FROM AUTHOR]

The distribution of the di erence between two independent Poisson random variables involves the modified Bessel function of the first kind. Using properties of this function, maximum likelihood estimates of the parameters of the Poisson di erence were derived. Asymptotic distribution property of the maximum likelihood estimates is discussed. Maximum likelihood estimates were compared with the moment estimates in a Monte Carlo study. Hypothesis testing using likelihood ratio tests was considered. Some new formulas concerning the modified Bessel function of the first kind were provided. Alternative formulas for the probability mass function of the Poisson di erence (PD) distribution are introduced. Finally, two new applications for the PD distribution are presented. The first is from the Saudi stock exchange (TASI) and the second is from Dallah hospital. [ABSTRACT FROM AUTHOR]

In this paper, based on the white noise theory for d-parameter Lévy random fields given by (Holden et al. in Stochastic Partial Differential Equations: A modeling, white noise functional approach, 2010), we develop a white noise frame for anisotropic fractional Lévy random fields to solve the stochastic Poisson equation and the stochastic Schrödinger equation driven by the d-parameter fractional Lévy noise. The solutions for the two kinds of equations are all strong solutions given explicitly in the Lévy-Hida stochastic distribution space. [ABSTRACT FROM AUTHOR]