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Several models for count time series have been developed during the last decades, often inspired by traditional autoregressive moving average (ARMA) models for real‐valued time series, including integer‐valued ARMA (INARMA) and integer‐valued generalized autoregressive conditional heteroscedasticity (INGARCH) models. Both INARMA and INGARCH models exhibit an ARMA‐like autocorrelation function (ACF). To achieve negative ACF values within the class of INGARCH models, log and softplus link functions are suggested in the literature, where the softplus approach leads to conditional linearity in good approximation. However, the softplus approach is limited to the INGARCH family for unbounded counts, that is, it can neither be used for bounded counts, nor for count processes from the INARMA family. In this paper, we present an alternative solution, named the Tobit approach, for achieving approximate linearity together with negative ACF values, which is more generally applicable than the softplus approach. A Skellam–Tobit INGARCH model for unbounded counts is studied in detail, including stationarity, approximate computation of moments, maximum likelihood and censored least absolute deviations estimation for unknown parameters and corresponding simulations. Extensions of the Tobit approach to other situations are also discussed, including underlying discrete distributions, INAR models, and bounded counts. Three real‐data examples are considered to illustrate the usefulness of the new approach. [ABSTRACT FROM AUTHOR]

The Skellam distribution is a discrete probability distribution related to the difference between two independent Poisson-distributed random variables. It has been used in a variety of contexts, including sports or supply and demand imbalances in shared transportation. Stata does not support the Skellam distribution or Skellam regression. We present a command, skellamreg, to estimate the parameters of a Skellam distribution and Skellam regression model using Mata's optimize function. [ABSTRACT FROM AUTHOR]

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]

Competitive balance in a football league is extremely important from the perspective of economic growth of the industry. Many researchers have earlier proposed different measures of competitive balance, which are primarily adapted from standard economic theory. However, these measures fail to capture the finer nuances of the game. In this work, we discuss a new framework which is more suitable for a football league. First, we present a mathematical proof of a theoretically optimal situation where a football league becomes perfectly balanced. Next, a goal based index for competitive balance is developed. We present relevant theoretical results and show how the proposed index can be used to formally test for the presence of imbalance. The methods are implemented on the data from the top five European leagues, and it shows that the new approach can be helpful in explaining the changes in the seasonal competitive balance of the leagues. Further, using panel data models, we show that the proposed index is more suitable to analyze the variability in total revenues of the football leagues. We also discuss how the methods can be easily extended to develop other goal-based indices under different modeling assumptions. [ABSTRACT FROM AUTHOR]

Estimation of latent network flows is a common problem in statistical network analysis. The typical setting is that we know the margins of the network, that is, in- and outdegrees, but the flows are unobserved. In this article, we develop a mixed regression model to estimate network flows in a bike-sharing network if only the hourly differences of in- and outdegrees at bike stations are known. We also include exogenous covariates such as weather conditions. Two different parameterizations of the model are considered to estimate (a) the whole network flow and (b) the network margins only. The estimation of the model parameters is proposed via an iterative penalized maximum likelihood approach. This is exemplified by modelling network flows in the Vienna bike-sharing system. In order to evaluate our modelling approach, we conduct our analyses exploiting different distributional assumptions while we also respect the provider's interventions appropriately for keeping the estimation error low. Furthermore, a simulation study is conducted to show the performance of the model. For practical purposes, it is crucial to predict when and at which station there is a lack or an excess of bikes. For this application, our model shows to be well suited by providing quite accurate predictions. [ABSTRACT FROM AUTHOR]

The tick structure of the financial markets entails discreteness of stock price changes. Based on this empirical evidence, we develop a multivariate model for discrete price changes featuring a mechanism to account for the large share of zero returns at high frequency. We assume that the observed price changes are independent conditional on the realization of two hidden Markov chains determining the dynamics and the distribution of the multivariate time series at hand. We study the properties of the model, which is a dynamic mixture of zero-inflated Skellam distributions. We develop an expectation-maximization algorithm with closed-form M-step that allows us to estimate the model by maximum likelihood. In the empirical application, we study the joint distribution of the price changes of a number of assets traded on NYSE. Particular focus is dedicated to the assessment of the quality of univariate and multivariate density forecasts, and of the precision of the predictions of moments like volatility and correlations. Finally, we look at the predictability of price staleness and its determinants in relation to the trading activity on the financial markets. [ABSTRACT FROM AUTHOR]

With the beginning of the COVID-19 pandemic, we became aware of the need for comprehensive data collection and its provision to scientists and experts for proper data analyses. In Germany, the Robert Koch Institute (RKI) has tried to keep up with this demand for data on COVID-19, but there were (and still are) relevant data missing that are needed to understand the whole picture of the pandemic. In this article, we take a closer look at the severity of the course of COVID-19 in Germany, for which ideal information would be the number of incoming patients to ICU units. This information was (and still is) not available. Instead, the current occupancy of ICU units on the district level was reported daily. We demonstrate how this information can be used to predict the number of incoming as well as released COVID-19 patients using a stochastic version of the Expectation Maximization algorithm (SEM). This, in turn, allows for estimating the influence of district-specific and age-specific infection rates as well as further covariates, including spatial effects, on the number of incoming patients. The article demon-strates that even if relevant data are not recorded or provided officially, statistical modelling allows for reconstructing them. This also includes the quantification of uncertainty which naturally results from the application of the SEM algorithm. [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]

A discrete version of the Gumbel distribution (Type-I Extreme Value distribution) has been derived by using the general approach of discretization of a continuous distribution. Important distributional and reliability properties have been explored. It has been shown that depending on the choice of parameters the proposed distribution can be positively or negatively skewed; possess long-tail(s). Log-concavity of the distribution and consequent results have been established. Estimation of parameters by method of maximum likelihood, method of moments, and method of proportions has been discussed. A method of checking model adequacy and regression type estimation based on empirical survival function has also been examined. A simulation study has been carried out to compare and check the efficacy of the three methods of estimations. The distribution has been applied to model three real count data sets from diverse application area namely, survival times in number of days, maximum annual floods data from Brazil and goal differences in English premier league, and the results show the relevance of the proposed distribution. [ABSTRACT FROM AUTHOR]

In this paper, we established a hyperbolically quasi-isometric inequality for quasiconformal twice continuously differentiable self-mappings f of unit disk satisfying Poisson differential inequality. Moreover, the co-Lipschitz continuity with respect to Euclidean metric for this class of functions was derived. [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]

A Monte Carlo SPICE framework is proposed to evaluate the impact of negative bias temperature instability (NBTI) variability on performance and static power (${P}_{\text {S}}$) of static random access memory (SRAM) array on 14-nm node FinFETs. Gamma distribution is found to be applicable for NBTI-induced threshold voltage ($\Delta {V}_{T}$) and subthreshold slope ($\Delta $ SS) shifts by using data set from different sources. A compact variability model is proposed for the time evolution of mean and variance of NBTI distribution, considering any possible correlation between time zero and NBTI variability. The relative sensitivity of device and SRAM degradation are evaluated, by correlating SRAM static noise margin degradation to transistor level ${V}_{T}$ shift. The impact of $\Delta $ SS on ${P}_{\text {S}}$ improvement due to NBTI is also evaluated. [ABSTRACT FROM AUTHOR]

This paper deals with development of diffusive propagation model for molecular communication in composite biological microenvironments with multiple regions (or layers) each with distinct diffusion properties to understand the transport of information molecules. We propose generalized analytical and simulation approaches for modeling a composite, diffusive, and molecular communication channel for arbitrary placement of the transmitting and receiving nano-machines. We derive a generalized closed-form expression for the channel impulse response of a three dimensionally (3-D) diffusive medium that has “N” regions. The results from the proposed particle-based simulator are validated with the exact analytical solution. The pulse peak amplitude, pulse peak time, and pulse width are derived to evaluate the system performance using both analytical and simulation approaches. It is shown that the channel impulse response and other communication metrics are significantly affected by the diffusion coefficients, region thickness, interface properties, and the positions of transmitter and receiver nano-machines with respect to the interfaces. [ABSTRACT FROM AUTHOR]

Summary: The scoring and defensive abilities of Australian Rules Football teams change over time as a result of evolving player rosters, tactics and other management factors. We develop a dynamic model based on the Poisson difference (Skellam) distribution which simultaneously models the two different point scoring mechanisms in Australian Rules Football, the motivation for which comes from work on predicting outcomes in soccer matches. Our model is developed in a Bayesian framework and is fitted using the Stan modelling language. Model validation is performed on the 2015 Australian Football league (AFL) home and away season. [ABSTRACT FROM AUTHOR]

The charge transport in an environment with inhomogeneous dielectric permittivity is ubiquitous in many areas such as electrochemical energy devices and biophysical systems. We theoretically study the equilibrium and dynamics of electrolytes between two blocking electrodes based on a modified Poisson--Nernst--Planck model with the dielectric boundary effect. Matched asymptotic analysis shows that a two-layer interfacial structure exists in the vicinity of the interfaces when the dielectric self-energy correction to the potential mean force is relatively weak. For this two-layer structured solution, the dielectric effect plays the dominate role in the first layer, while the solution in the second layer is mainly determined by the classical Poisson--Boltzmann equation. When the dielectric self energy becomes stronger, there is only one interfacial layer which is governed by the modified Poisson--Boltzmann equation with the dielectric self-energy correction in the Boltzmann factor. We perform a systematic investigation for symmetric and asymmetric electrolytes on ionic concentrations, electrostatic potential, diffuse charges, differential capacitance, and charge inversion phenomenon to show the effects of the dielectric inhomogeneity on the solutions near interfaces. [ABSTRACT FROM AUTHOR]

The dynamical model of the nonlinear acoustic wave in rotating magnetized plasma is governed by a partial differential equation system. Its traveling system is a singular traveling wave system of first class depending on two parameters. By using the bifurcation theory and method of dynamical systems and the theory of singular traveling wave systems, in this paper, we show that there exist parameter groups such that this singular system has pseudo-peakons, periodic peakons and compactons as well as different solitary wave solutions. [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]

We study intraday stochastic volatility for four liquid stocks traded on the New York Stock Exchange using a new dynamic Skellam model for high-frequency tick-by-tick discrete price changes. Since the likelihood function is analytically intractable, we rely on numericalmethods for its evaluation. Given the high number of observations per series per day (1000 to 10,000), we adopt computationally efficient methods including Monte Carlo integration. The intraday dynamics of volatility and the high number of trades without price impact require nontrivial adjustments to the basic dynamic Skellam model. In-sample residual diagnostics and goodness-of-fit statistics show that the final model provides a good fit to the data. An extensive dayto- day forecasting study of intraday volatility shows that the dynamic modified Skellam model provides accurate forecasts compared to alternative modeling approaches. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

We study the boundary layer problem and the quasineutral limit of the compressible Euler-Poisson system arising from plasma physics in a domain with boundary. The quasineutral regime is the incompressible Euler equations. Compared to the quasineutral limit of compressible Euler-Poisson equations in whole space or periodic domain, the key difficulty here is to deal with the singularity caused by the boundary layer. The proof of the result is based on a λ- weighted energy method and the matched asymptotic expansion method. [ABSTRACT FROM AUTHOR]

The Inter-Symbol Interference (ISI) in Diffusive Molecular Communication (DMC) is unavoidable due to the stochastic behavior of molecular Brownian motion in a biological environment. In this paper, we analyze the channel capacity of DMC model by considering the ISI from all the previous time slots and the channel transmission probability in each time slot. We first use the Poisson distribution to approximate the Binomial distribution in order to obtain the total number of molecules received in the current time slot. Then we derive the mathematical expressions of optimal decision threshold by using the Skellam distribution. On this basis, we formulate the mutual information and bit error probability. Our numerical results are presented to show the channel capacity can be maximized with optimal lower bit error probability by controlling the channel transmission probability in each time slot and using the Skellam distribution. More importantly, under the same physical parameters, a higher capacity is achieved with using fewer molecules in our work. [ABSTRACT FROM AUTHOR]

Relatively high counting rates were registered in a proton inelastic scattering experiment on 16 O and 28 Si using HPGe detectors which was performed at the Tandem facility of IFIN-HH, Bucharest. In consequence, dead time corrections were needed in order to determine the absolute γ -production cross sections. Considering that the real counting rate follows a Poisson distribution, the dead time correction procedure is reformulated in statistical terms. The arriving time interval between the incoming events ( Δ t ) obeys an exponential distribution with a single parameter - the average of the associated Poisson distribution. We use this mathematical connection to calculate and implement the dead time corrections for the counting rates of the mentioned experiment. Also, exploiting an idea introduced by Pommé et al. , we describe a consistent method for calculating the dead time correction which completely eludes the complicated problem of measuring the dead time of a given detection system. Several comparisons are made between the corrections implemented through this method and by using standard (phenomenological) dead time models and we show how these results were used for correcting our experimental cross sections. [ABSTRACT FROM AUTHOR]

Our work in this paper is inspired by a statistical observation that is both elementary and broadly relevant to network analysis in practice--that the uncertainty in approximating some true graph G = (V, E) by some estimated graph G = (V, E) manifests as errors in our knowledge of the presence/absence of edges between vertex pairs, which must necessarily propagate to any estimates of network summaries n(G) we seek. Motivated by the common practice of using plug-in estimates n(G) as proxies for n(G), our focus is on the problem of characterizing the distribution of the discrepancy n = r/(G) - n(G), in the case where n( ) is a subgraph count. Specifically, we study the fundamental case where the statistic of interest is |E|, the number of edges in G. Our primary contribution in this paper is to show that in the empirically relevant setting of large graphs with low-rate measurement errors, the distribution of DE = |E| -- |E| is well-characterized by a Skellam distribution, when the errors are independent or weakly dependent. under an assumption of independent errors, we are able to further show conditions under which this characterization is strictly better than that of an appropriate normal distribution. These results derive from our formulation of a general result, quantifying the accuracy with which the difference of two sums of dependent Bernoulli random variables may be approximated by the difference of two independent Poisson random variables, i.e., by a Skellam distribution. This general result is developed through the use of Stein's method, and may be of some general interest. We finish with a discussion of possible extension of our work to subgraph counts n(G) of higher order. [ABSTRACT FROM AUTHOR]

In this paper, a novel graphics-processing unit (GPU) implementation of the recently proposed correction function method (CFM) is presented, for the finite-difference solution of Poisson problems with surface-charge distributions. The CFM is a robust and versatile method most notable for its immersed treatment of interface problems of any geometry, to an arbitrary order of accuracy. Given the well-known interface jump conditions associated with the electric scalar potential, the CFM is here shown to be immediately applicable to the computation of electrostatic fields, in the presence of curved surface-charge distributions. Moreover, an in-depth analysis of the CFM algorithm is presented, in which performance bottlenecks are investigated and significant potential for parallelizability is identified. The resulting parallel CFM algorithm is then implemented using NVIDIA’s compute unified device architecture GPU language, yielding a significant increase in performance. [ABSTRACT FROM AUTHOR]

This paper derives and compares two competing-destinations formulation of the gravity model applied to trade in intermediates. We build a probabilistic input demand function from entropy maximization in which firms may purchase some of their inputs from other firms paying the required transport costs and accounting for the spatial structure of trading partners in a geographical system. In the second model, firms trade inputs to reduce the overall cost of production and intermediate sales are encouraged by low distance costs and low competition from alternative input sources. Even if the gravity equations look similar, we show that their underlying structures are different, and that the type of gravity equation has significant implications for the estimation technique adopted. [ABSTRACT FROM PUBLISHER]

Moving averages are a common method of forecasting futures basis. We argue that the optimal lengths of moving averages depend on the frequency of structural breaks. A new stochastic time-series process including structural breaks is modelled by discrete probability distributions that capture the frequency and size of structural breaks. A permanent shock (means structural breaks in this article) is captured by a Poisson-jump or a Bernoulli-jump process, and a temporary shock is represented by a white noise process. Futures basis data are used to estimate the frequency of permanent shocks as well as the size of both shocks. Most shocks are permanent shocks. Since most shocks are permanent, the most recent year provides the best forecast and the optimal length of the moving average is one. [ABSTRACT FROM PUBLISHER]

The effects of volume corrections and resonance decays (the resulting correlations between positive charges and negative charges) on cumulants of net-proton distributions and net-charge distributions are investigated by using a Monte Carlo hadron resonance gas ( MCHRG ) model. The required volume distributions are generated by a Monte Carlo Glauber ( MC-Glb ) model. Except the variances of net-charge distributions, the MCHRG model with more realistic simulations of volume corrections, resonance decays and acceptance cuts can reasonably explain the data of cumulants of net-proton distributions and net-charge distributions reported by the STAR collaboration. The MCHRG calculations indicate that both the volume corrections and resonance decays make the cumulant products of net-charge distributions deviate from the Skellam expectations: the deviations of Sσ and κ σ 2 are dominated by the former effect while the deviations of ω are dominated by the latter one. [ABSTRACT FROM AUTHOR]

Two bivariate extensions of the Skellam distribution were introduced in 2014 by a subset of the present authors, who also proposed moment estimators for the dependence parameters in these models. The limiting distribution of these estimators is established here, and their asymptotic efficiency is compared with that of the corresponding maximum likelihood estimators. © 2017 The Authors. Stat Published by John Wiley & Sons Ltd. [ABSTRACT FROM AUTHOR]

In this article we discuss a pointwise superconvergence post-processing technique for the gradient of the trilinear block finite element for the Poisson equation with homogeneous Dirichlet boundary conditions over a fully uniform mesh of the three-dimensional domain Ω. First, the supercloseness of the gradients between the piecewise trilinear finite element solution uh and the trilinear interpolant Πu is given. Secondly, we analyze a superconvergence post-processing scheme for the gradient of the finite element solution by using the Z-Z recovery technique, which shows that the recovered gradient of uh is superconvergent to the gradient of the true solution u in the pointwise sense of the L∞-norm. Finally, a numerical example is given. [ABSTRACT FROM AUTHOR]

This paper employs a Skellam process to represent real-time betting odds for English Premier League (EPL) soccer games. Given a matrix of market odds on all possible score outcomes, we estimate the expected scoring rates for each team. The expected scoring rates then define the implied volatility of an EPL game. As events in the game evolve, we re-estimate the expected scoring rates and our implied volatility measure to provide a dynamic representation of the market's expectation of the game outcome. Using a dataset of 1520 EPL games from 2012-2016, we show how our model calibrates well to the game outcome. We illustrate our methodology on real-time market odds data for a game between Everton andWestHamin the 2015-2016 season. We show how the implied volatility for the outcome evolves as goals, red cards, and corner kicks occur. Finally, we conclude with directions for future research. [ABSTRACT FROM AUTHOR]

The Poisson distribution is extended over the set of all integers. The motivation comes from the many reflected versions of the gamma distribution, the continuous analog of the Poisson distribution, defined over the entire real line. Various mathematical properties of the extended Poisson distribution are derived. Estimation procedures by the methods of moments and maximum likelihood are also derived with their performance assessed by simulation. Finally, a real data application is illustrated. [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]

The analysis of sports data, in particular football match outcomes, has always produced an immense interest among the statisticians. In this paper, we adopt the generalized Poisson difference distribution (GPDD) to model the goal difference of football matches. We discuss the advantages of the proposed model over the Poisson difference (PD) model, which was also used for the same purpose. The GPDD model, like the PD model, is based on the goal difference in each game that allows us to account for the correlation without explicitly modelling it. The main advantage of the GPDD model is its flexibility in the tails by considering shorter as well as longer tails than the PD distribution. We carry out the analysis in a Bayesian framework in order to incorporate external information, such as historical knowledge or data, through the prior distributions. We model both the mean and the variance of the goal difference and show that such a model performs considerably better than a model with a fixed variance. Finally, the proposed model is fitted to the 2012–2013 Italian Serie A football data, and various model diagnostics are carried out to evaluate the performance of the model. [ABSTRACT FROM AUTHOR]

This paper is concerned with the three dimensional compressible Euler–Poisson equations with moving physical vacuum boundary condition. This fluid system is usually used to describe the motion of a self-gravitating inviscid gaseous star. The local existence of classical solutions for initial data in certain weighted Sobolev spaces is established in the case that the adiabatic index satisfies 1 < γ < 3 . [ABSTRACT FROM AUTHOR]

Confusions between drug names that look and sound alike are common, costly, harmful, and difficult to prevent. One prevention strategy is to screen proposed new drug names for confusability before approving them. Widespread acceptance of preapproval tests of confusability is compromised by the lack of experimental designs and statistical methods to support valid inferences about whether a proposed new name is unacceptably confusing. One way of identifying confusing names is to conduct memory and perception experiments on a set of drug names which would include both the new name and a set of control names (e.g., names already on the market). The experiment would yield an observed error rate for every name. Inferences about the acceptability of the new name can be made by comparing the error rate of the new name to the distribution of error rates of the control names. We describe four memory and perception experiments on drug names, carried out using clinicians as participants. Each experiment included drug names designated as test and control names. We demonstrate how to use a combination of logistic regression, Poisson prediction limits, and highly assured credible intervals to identify and apply a threshold for identifying unacceptably confusing names. Our models show an excellent fit to the data. These experimental designs and analytic methods should be useful in the preapproval testing of proposed new drug names and in similar regulatory scenarios where it is necessary to draw inferences about the comparative safety or effectiveness of new vs. old products. [ABSTRACT FROM PUBLISHER]

A new discrete probability distribution with integer support on (−∞, ∞) is proposed as a discrete analog of the continuous logistic distribution. Some of its important distributional and reliability properties are established. Its relationship with some known distributions is discussed. Parameter estimation by maximum-likelihood method is presented. Simulation is done to investigate properties of maximum-likelihood estimators. Real life application of the proposed distribution as empirical model is considered by conducting a comparative data fitting with Skellam distribution, Kemp's discrete normal, Roy's discrete normal, and discrete Laplace distribution. [ABSTRACT FROM AUTHOR]

The free energy of the charged drops of water and of light ions inside drop-ionic plasma of clouds and fog was calculated on the basis of the Poisson–Boltzmann equation. It is shown that when the charge is greater than several tens of elementary charge units, the positively and negatively charged drops can have metastable states which are characterized by the space-ordered arrangement of the drops. In general, the drop-ionic plasma has no metastable state. But, in the case that the average charges of positively and negatively charged drops differ in absolute value by less than 10–20%, drop-ionic plasma can have a metastable state as a whole. This state was thought to be responsible for the long confinement of drops in a compact volume and for their subsequent coalescence. It is shown that the electrostatic attraction of drops and their coalescence are capable of explaining the rapid growth of water drops up to rain size inside clouds. [ABSTRACT FROM AUTHOR]

We have given an extension to the study of Kierstead, Slobodkin, and Skellam (KiSS) model. We present the theoretical results based on the survival and permanence of the species. To guarantee the long-term existence and permanence, the patch size denoted as L must be greater than the critical patch size Lc. It was also observed that the reaction-diffusion problem can be split into two parts: the linear and nonlinear terms. Hence, the use of two classical methods in space and time is permitted. We use spectral method in the area of mathematical community to remove the stiffness associated with the linear or diffusive terms. The resulting system is advanced with a modified exponential time-differencing method whose formulation was based on the fourth-order Runge-Kutta scheme. With high-order method, this extends the one-dimensional work and presents experiments for two-dimensional problem. The complexity of the dynamical model is discussed theoretically and graphically simulated to demonstrate and compare the behavior of the time-dependent density function. [ABSTRACT FROM AUTHOR]

In this article, we introduce a new distribution on, which can be viewed as a natural bivariate extension of the Skellam distribution. The main feature of this distribution a possible dependence of the univariate components, both following univariate Skellam distributions. We explore various properties of the distribution and investigate the estimation of the unknown parameters via the method of moments and maximum likelihood. In the experimental section, we illustrate our theory. First, we compare the performance of the estimators by means of a simulation study. In the second part, we present two applications to a real data set and show how an improved fit can be achieved by estimating mixture distributions. [ABSTRACT FROM PUBLISHER]