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The expected goal provides a more representative measure of the team and player performance which also suit the low-scoring nature of football instead of score in modern football. The score of a match involves randomness and often may not…
The explosion of mobile phone communications in the last years occurs at a moment where data processing power increases exponentially. Thanks to those two changes in a global scale, the road has been opened to use mobile phone…
Quarterback performance can be difficult to rank, and much effort has been spent in creating new rating systems. However, the input statistics for such ratings are subject to randomness and factors outside the quarterback's control. To…
This paper reviews and compares popular methods, some old and some very recent, that produce time series having Poisson marginal distributions. The paper begins by narrating ways where time series with Poisson marginal distributions can be…
In the sport of cricket, variations in a player's batting ability can usually be measured on one of two scales. Short-term changes in ability that are observed during a single innings, and long-term changes that are witnessed between…
The mathematical properties of a family of generalized beta distribution, including beta-normal, skewed-t, log-F, beta-exponential, beta-Weibull distributions have recently been studied in several publications. This paper applies these…
We consider the problem of frequency estimation by observations of the periodic diffusion process possesing ergodic properties in two different situations. The first one corresponds to continuously differentiable with respect to parameter…
The importance of the ability of predict trends in social media has been growing rapidly in the past few years with the growing dominance of social media in our everyday's life. Whereas many works focus on the detection of anomalies in…
If we know that some kind of sequence always converges, we can ask how quickly and how uniformly it converges. Many convergent sequences converge non-uniformly and, relatedly, have no computable rate of convergence. However proof-theoretic…
The \textit{ternary digits of $2^n$} are a finite sequence of 0s, 1s, and 2s. It is a natural question to ask whether the frequency of any string of 0s, 1s, and 2s in this sequence approaches the same limit for all strings of the same…
This paper synthesises the existing research on the dynamics of innovation diffusion, with a focus on Bass-type models and their extensions. The theoretical foundation of innovation diffusion proposed by Rogers (1962) and the seminal work…
We consider a general class of random matrices whose entries are centred random variables, independent up to a symmetry constraint. We establish precise high-probability bounds on the averages of arbitrary monomials in the resolvent matrix…
Forecasting sporting events encapsulate a compelling intellectual endeavor, underscored by the substantial financial activity of an estimated $80 billion wagered in global sports betting during 2022, a trend that grows yearly. Motivated by…
Recently it has become clear that many technologies follow a generalized version of Moore's law, i.e. costs tend to drop exponentially, at different rates that depend on the technology. Here we formulate Moore's law as a correlated…
The spread of infectious disease in a human community or the proliferation of fake news on social media can be modeled as a randomly growing tree-shaped graph. The history of the random growth process is often unobserved but contains…
The widely claimed replicability crisis in science may lead to revised standards of significance. The customary frequentist confidence intervals, calibrated through hypothetical repetitions of the experiment that is supposed to have…
The goal of this study is to explain and examine the statistical underpinnings of the Bollinger Band methodology. We start off by elucidating the rolling regression time series model and deriving its explicit relationship to Bollinger…
Using the lag-luminosity relation and various BATSE catalogs we create a large catalog of burst redshifts, peak luminosities and emitted energies. These catalogs permit us to evaluate the lag-luminosity relation, and to study the burst…
Existing approaches for estimating home-field advantage (HFA) include modeling the difference between home and away scores as a function of the difference between home and away team ratings that are treated either as fixed or random…
The infield shift has been increasingly used as a defensive strategy in baseball in recent years. Along with the upward trend in its usage, the notoriety of the shift has grown, as it is believed to be responsible for the recent decline in…