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Non-extensive Entropy Econometrics for Low Frequency Series provides a new and robust power-law-based, non-extensive entropy econometrics approach to the economic modelling of ill-behaved inverse problems. Particular attention is paid to national account-based general equilibrium models known for their relative complexity.In theoretical terms, the approach generalizes Gibbs-Shannon-Golan entropy models, which are useful for describing ergodic phenomena. In essence, this entropy econometrics approach constitutes a junction of two distinct concepts: Jayne's maximum entropy principle and the Bayesian generalized method of moments. Rival econometric techniques are not conceptually adapted to solving complex inverse problems or are seriously limited when it comes to practical implementation. Recent literature showed that amplitude and frequency of macroeconomic fluctuations do not substantially diverge from many other extreme events, natural or human-related, once they are explained in the same time (or space) scale. Non-extensive entropy is a precious device for econometric modelling even in the case of low frequency series, since outputs evolving within the Gaussian attractor correspond to the Tsallis entropy limiting case of Tsallis q-parameter around unity. This book introduces a sub-discipline called Non-extensive Entropy Econometrics or, using a recent expression, Superstar Generalised Econometrics. It demonstrates, using national accounts-based models, that this approach facilitates solving nonlinear, complex inverse problems, previously considered intractable, such as the constant elasticity of substitution class of functions. This new proposed approach could extend the frontier of theoretical and applied econometrics.

Business cycles. --- Econometrics. --- Maximum entropy method. --- generalized cross-entropy, general equilibrium macro-economic model, econometrics. --- BUSINESS & ECONOMICS / Econometrics. --- Entropy maximization --- Entropy maximum principle --- Maximization, Entropy --- Entropy (Information theory) --- Maximum principles (Mathematics) --- Economics, Mathematical --- Statistics --- Economic cycles --- Economic fluctuations --- Cycles

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This book establishes several weak limit laws for problems in geometric extreme value theory. We find the limit law of the maximum Euclidean distance of i.i.d. points, as the number of points tends to infinity, under certain assumptions on the underlying distribution. One of the methods is also applicable for some other functionals, such as the maximum area or the maximum perimeter of triangles formed by point triplets.

limit distribution --- random point set --- maximum distance --- Poisson approximation --- geometric extreme value theory

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In recent years, the advances and abilities of computer software have substantially increased the number of scientific publications that seek to introduce new probabilistic modelling frameworks, including continuous and discrete approaches, and univariate and multivariate models. Many of these theoretical and applied statistical works are related to distributions that try to break the symmetry of the normal distribution and other similar symmetric models, mainly using Azzalini's scheme. This strategy uses a symmetric distribution as a baseline case, then an extra parameter is added to the parent model to control the skewness of the new family of probability distributions. The most widespread and popular model is the one based on the normal distribution that produces the skewed normal distribution. In this Special Issue on symmetric and asymmetric distributions, works related to this topic are presented, as well as theoretical and applied proposals that have connections with and implications for this topic. Immediate applications of this line of work include different scenarios such as economics, environmental sciences, biometrics, engineering, health, etc. This Special Issue comprises nine works that follow this methodology derived using a simple process while retaining the rigor that the subject deserves. Readers of this Issue will surely find future lines of work that will enable them to achieve fruitful research results.

positive and negative skewness --- ordering --- fitting distributions --- Epsilon-skew-Normal --- Epsilon-skew-Cauchy --- bivariate densities --- generalized Cauchy distributions --- asymmetric bimodal distribution --- bimodal --- maximum likelihood --- slashed half-normal distribution --- kurtosis --- likelihood --- EM algorithm --- flexible skew-normal distribution --- skew Birnbaum–Saunders distribution --- bimodality --- maximum likelihood estimation --- Fisher information matrix --- maximum likelihood estimates --- type I and II censoring --- skewness coefficient --- Weibull censored data --- truncation --- half-normal distribution --- probabilistic distribution class --- normal distribution --- identifiability --- moments --- power-normal distribution

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The solution of various tasks benefits from information fusion or even requires it. The Bayesian fusion methodology is clear, well-founded and fulfills the essential requirements for a meaningful methodology also for fusing the contributions of heterogeneous information sources. In many practically relevant tasks, Bayesian methods cause high, often unacceptable effort. In the work, novel approaches to cope with Bayesian fusion in such situations are formulated and investigated.

Maths for computer scientists --- Informationsfusion --- heterogene Informationsquellen --- Bayes’sche Theorie --- Prinzip der Maximalen Entropie --- Unsicherheit --- information fusion --- heterogeneous information sources --- Bayesian theory --- Maximum Entropy principle --- uncertainty

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Research without statistics is like water in the sand; the latter is necessary to reap the benefits of the former. This collection of articles is designed to bring together different approaches to applied statistics. The studies presented in this book are a tiny piece of what applied statistics means and how statistical methods find their usefulness in different fields of research from theoretical frames to practical applications such as genetics, computational chemistry, and experimental design. This book presents several applications of the statistics: A new continuous distribution with five parameters—the modified beta Gompertz distribution; A method to calculate the p-value associated with the Anderson–Darling statistic; An approach of repeated measurement designs; A validated model to predict statement mutations score; A new family of structural descriptors, called the extending characteristic polynomial (EChP) family, used to express the link between the structure of a compound and its properties. This collection brings together authors from Europe and Asia with a specific contribution to the knowledge in regards to theoretical and applied statistics.

molecular descriptors --- compound symmetry --- Anderson–Darling test (AD) --- software testing --- probability --- characteristic polynomial (ChP) --- mutation testing --- C20 fullerene --- fullerene congeners --- machine learning --- maximum likelihood estimation --- gompertz distribution --- modified beta generator --- structure–property relationships --- repeated measurement designs --- Monte Carlo simulation