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This book is summarizing the results of the workshop "Uniform Distribution and Quasi-Monte Carlo Methods" of the RICAM Special Semester on "Applications of Algebra and Number Theory" in October 2013. The survey articles in this book focus on number theoretic point constructions, uniform distribution theory, and quasi-Monte Carlo methods. As deterministic versions of the Monte Carlo method, quasi-Monte Carlo rules enjoy increasing popularity, with many fruitful applications in mathematical practice, as for example in finance, computer graphics, and biology. The goal of this book is to give an overview of recent developments in uniform distribution theory, quasi-Monte Carlo methods, and their applications, presented by leading experts in these vivid fields of research.
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Interest in the skew-normal and related families of distributions has grown enormously over recent years, as theory has advanced, challenges of data have grown, and computational tools have made substantial progress. This comprehensive treatment, blending theory and practice, will be the standard resource for statisticians and applied researchers. Assuming only basic knowledge of (non-measure-theoretic) probability and statistical inference, the book is accessible to the wide range of researchers who use statistical modelling techniques. Guiding readers through the main concepts and results, it covers both the probability and the statistics sides of the subject, in the univariate and multivariate settings. The theoretical development is complemented by numerous illustrations and applications to a range of fields including quantitative finance, medical statistics, environmental risk studies, and industrial and business efficiency. The author's freely available R package sn, available from CRAN, equips readers to put the methods into action with their own data.
Distribution (Probability theory) --- Mathematics --- Probability theory --- Mathematical Sciences --- Probability
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Jason Gibson explains how to use a sampling distribution. He starts by defining the sampling distribution, then continues into how a student might find a sampling distribution in practice.
Distribution (Probability theory) --- Mathematical statistics. --- Research --- Statistical methods.
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Interest in the skew-normal and related families of distributions has grown enormously over recent years, as theory has advanced, challenges of data have grown, and computational tools have made substantial progress. This comprehensive treatment, blending theory and practice, will be the standard resource for statisticians and applied researchers. Assuming only basic knowledge of (non-measure-theoretic) probability and statistical inference, the book is accessible to the wide range of researchers who use statistical modelling techniques. Guiding readers through the main concepts and results, it covers both the probability and the statistics sides of the subject, in the univariate and multivariate settings. The theoretical development is complemented by numerous illustrations and applications to a range of fields including quantitative finance, medical statistics, environmental risk studies, and industrial and business efficiency. The author's freely available R package sn, available from CRAN, equips readers to put the methods into action with their own data.
Distribution (Probability theory) --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Mathematical Sciences --- Probability
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This textbook is devoted to the general asymptotic theory of statistical experiments. Local asymptotics for statistical models in the sense of local asymptotic (mixed) normality or local asymptotic quadraticity make up the core of the book. Numerous examples deal with classical independent and identically distributed models and with stochastic processes. The book can be read in different ways, according to possibly different mathematical preferences of the reader. One reader may focus on the statistical theory, and thus on the chapters about Gaussian shift models, mixed normal and quadratic models, and on local asymptotics where the limit model is a Gaussian shift or a mixed normal or a quadratic experiment (LAN, LAMN, LAQ). Another reader may prefer an introduction to stochastic process models where given statistical results apply, and thus concentrate on subsections or chapters on likelihood ratio processes and some diffusion type models where LAN, LAMN or LAQ occurs. Finally, readers might put together both aspects. The book is suitable for graduate students starting to work in statistics of stochastic processes, as well as for researchers interested in a precise introduction to this area.
Mathematical statistics --- Asymptotic distribution (Probability theory) --- Asymptotic expansions --- Central limit theorem --- Distribution (Probability theory) --- Asymptotic theory. --- General Asymptotic Theory. --- LAMN. --- LAN. --- LAQ. --- Local Asymptotic Normality. --- Local Asymptotic Quadraticity. --- Local Asymptotic. --- Statistical Experiment. --- Statistical Model.
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This work is unique as it provides a uniform treatment of the Fourier theories of functions (Fourier transforms and series, z-transforms), finite measures (characteristic functions, convergence in distribution), and stochastic processes (including arma series and point processes). It emphasises the links between these three themes. The chapter on the Fourier theory of point processes and signals structured by point processes is a novel addition to the literature on Fourier analysis of stochastic processes. It also connects the theory with recent lines of research such as biological spike signals and ultrawide-band communications. Although the treatment is mathematically rigorous, the convivial style makes the book accessible to a large audience. In particular, it will be interesting to anyone working in electrical engineering and communications, biology (point process signals) and econometrics (arma models). A careful review of the prerequisites (integration and probability theory in the appendix, Hilbert spaces in the first chapter) make the book self-contained. Each chapter has an exercise section, which makes Fourier Analysis and Stochastic Processes suitable for a graduate course in applied mathematics, as well as for self-study.
Fourier analysis. --- Mathematics. --- Distribution (Probability theory) --- Probability Theory and Stochastic Processes. --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Analysis, Fourier --- Math --- Distribution functions --- Frequency distribution --- Probabilities. --- Fourier Analysis. --- Fourier Analysis --- Distribution (Probability theory). --- Mathématiques --- Analyse de Fourier --- Distribution (Théorie des probabilités) --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B --- Distribution (Probability theory. --- Mathematical analysis --- Characteristic functions --- Probabilities --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk
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"Journal of Statistical Distributions and Applications is a peer-reviewed international journal for the publication of original articles of high quality that make significant contributions to statistical distributions and their applications. The scopes include, but are not limited to, development and study of statistical distributions, frequentest and Bayesian statistical inference including goodness-of-fit tests, statistical modeling, computational/simulation methods, and data analysis related to statistical distributions."
Distribution (Probability theory) --- Distribution (Théorie des probabilités) --- Periodicals --- Périodiques --- Distribution functions --- Frequency distribution --- statistics --- statistical modelling --- data analysis --- Characteristic functions --- Probabilities --- Mathematical Statistics --- Probability theory
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The goal of this Lecture Note is to prove a new type of limit theorems for normalized sums of strongly dependent random variables that play an important role in probability theory or in statistical physics. Here non-linear functionals of stationary Gaussian fields are considered, and it is shown that the theory of Wiener–Itô integrals provides a valuable tool in their study. More precisely, a version of these random integrals is introduced that enables us to combine the technique of random integrals and Fourier analysis. The most important results of this theory are presented together with some non-trivial limit theorems proved with their help. This work is a new, revised version of a previous volume written with the goalof giving a better explanation of some of the details and the motivation behind the proofs. It does not contain essentially new results; it was written to give a better insight to the old ones. In particular, a more detailed explanation of generalized fields is included to show that what is at the first sight a rather formal object is actually a useful tool for carrying out heuristic arguments.
Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Mathematics. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Stochastic integrals. --- Gaussian processes. --- Distribution (Probability theory) --- Stochastic processes --- Integrals, Stochastic --- Stochastic analysis --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk
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A highly readable introduction to stochastic integration and stochastic differential equations, this book combines developments of the basic theory with applications. It is written in a style suitable for the text of a graduate course in stochastic calculus, following a course in probability. Using the modern approach, the stochastic integral is defined for predictable integrands and local martingales; then Itô’s change of variable formula is developed for continuous martingales. Applications include a characterization of Brownian motion, Hermite polynomials of martingales, the Feynman–Kac functional and the Schrödinger equation. For Brownian motion, the topics of local time, reflected Brownian motion, and time change are discussed. New to the second edition are a discussion of the Cameron–Martin–Girsanov transformation and a final chapter which provides an introduction to stochastic differential equations, as well as many exercises for classroom use. This book will be a valuable resource to all mathematicians, statisticians, economists, and engineers employing the modern tools of stochastic analysis. The text also proves that stochastic integration has made an important impact on mathematical progress over the last decades and that stochastic calculus has become one of the most powerful tools in modern probability theory. —Journal of the American Statistical Association An attractive text…written in [a] lean and precise style…eminently readable. Especially pleasant are the care and attention devoted to details… A very fine book. —Mathematical Reviews .
Mathematics. --- Distribution (Probability theory) --- Probability Theory and Stochastic Processes. --- Stochastic integrals --- Martingales (Mathematics) --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Integrals, Stochastic --- Math --- Distribution functions --- Frequency distribution --- Probabilities. --- Stochastic integrals. --- Stochastic processes --- Stochastic analysis --- Distribution (Probability theory. --- Characteristic functions --- Probabilities --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk
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This text is for a one semester graduate course in statistical theory and covers minimal and complete sufficient statistics, maximum likelihood estimators, method of moments, bias and mean square error, uniform minimum variance estimators and the Cramer-Rao lower bound, an introduction to large sample theory, likelihood ratio tests and uniformly most powerful tests and the Neyman Pearson Lemma. A major goal of this text is to make these topics much more accessible to students by using the theory of exponential families. Exponential families, indicator functions and the support of the distribution are used throughout the text to simplify the theory. More than 50 ``brand name" distributions are used to illustrate the theory with many examples of exponential families, maximum likelihood estimators and uniformly minimum variance unbiased estimators. There are many homework problems with over 30 pages of solutions.
Statistics. --- Probabilities. --- Statistical Theory and Methods. --- Probability Theory and Stochastic Processes. --- Statistics, general. --- Mathematical statistics. --- Distribution (Probability theory. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Statistical inference --- Statistics, Mathematical --- Statistics --- Sampling (Statistics) --- Distribution (Probability theory) --- Statistics . --- Probability --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk
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