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Stein's startling technique for deriving probability approximations first appeared about 30 years ago. Since then, much has been done to refine and develop the method, but it is still a highly active field of research, with many outstanding problems, both theoretical and in applications. This volume, the proceedings of a workshop held in honour of Charles Stein in Singapore, August 2003, contains contributions from many of the mathematicians at the forefront of this effort. It provides a cross-section of the work currently being undertaken, with many pointers to future directions. The papers i
Distribution (Probability theory) --- Approximation theory --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities
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This book is a useful overview of results in multivariate probability distributions and multivariate analysis as well as a reference to harmonic analysis on symmetric cones adapted to the needs of researchers in analysis and probability theory.
Distribution (Probability theory) --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Data processing. --- Mathematical models.
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In a certain sense characteristic functions and correlation functions are the same, the common underlying concept is positive definiteness. Many results in probability theory, mathematical statistics and stochastic processes can be derived by using these functions. While there are books on characteristic functions of one variable, books devoting some sections to the multivariate case, and books treating the general case of locally compact groups, interestingly there is no book devoted entirely to the multidimensional case which is extremely important for applications. This book is intended to fill this gap at least partially. It makes the basic concepts and results on multivariate characteristic and correlation functions easily accessible to both students and researchers in a comprehensive manner. The first chapter presents basic results and should be read carefully since it is essential for the understanding of the subsequent chapters. The second chapter is devoted to correlation functions, their applications to stationary processes and some connections to harmonic analysis. In Chapter 3 we deal with several special properties, Chapter 4 is devoted to the extension problem while Chapter 5 contains a few applications. A relatively large appendix comprises topics like infinite products, functional equations, special functions or compact operators.
Characteristic functions. --- Correlation (Statistics) --- Variables (Mathematics) --- Multivariate analysis. --- Multivariate distributions --- Multivariate statistical analysis --- Statistical analysis, Multivariate --- Analysis of variance --- Mathematical statistics --- Matrices --- Mathematical constants --- Mathematics --- Least squares --- Probabilities --- Regression analysis --- Statistics --- Instrumental variables (Statistics) --- Characteristic formula of an ideal --- Characteristic Hilbert functions --- Functions, Characteristic --- Functions, Hilbert --- Hilbert characteristic functions --- Hilbert functions --- Hilbert's characteristic functions --- Hilbert's functions --- Postulation formula --- Graphic methods --- Characteristic Functions. --- Fourier Transform. --- Moment Problem. --- Probability Distribution.
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The Gibbs measure is a probability measure, which has been an important object in many problems of probability theory and statistical mechanics. It is the measure associated with the Hamiltonian of a physical system (a model) and generalizes the notion of a canonical ensemble. More importantly, when the Hamiltonian can be written as a sum of parts, the Gibbs measure has the Markov property (a certain kind of statistical independence), thus leading to its widespread appearance in many problems outside of physics such as biology, Hopfield networks, Markov networks, and Markov logic networks. Mor
Probability measures. --- Distribution (Probability theory) --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Measures, Normalized --- Measures, Probability --- Normalized measures
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Distribution (Probability theory) --- Distribution (Théorie des probabilités) --- 519.213 --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Probability distributions and densities. Normal distribution. Characteristic functions. Measures of dependence. Infinitely divisible laws. Stable laws --- Distribution (Probability theory). --- 519.213 Probability distributions and densities. Normal distribution. Characteristic functions. Measures of dependence. Infinitely divisible laws. Stable laws --- Distribution (Théorie des probabilités)
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Analytical spaces --- Probability theory --- Distribution (Probability theory) --- Linear topological spaces --- 519.213 --- Topological linear spaces --- Topological vector spaces --- Vector topology --- Topology --- Vector spaces --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Probability distributions and densities. Normal distribution. Characteristic functions. Measures of dependence. Infinitely divisible laws. Stable laws --- 519.213 Probability distributions and densities. Normal distribution. Characteristic functions. Measures of dependence. Infinitely divisible laws. Stable laws --- Measure theory --- Mesure, Théorie de la --- Mesure, Théorie de la. --- Distribution (théorie des probabilités)
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Probability theory --- Stochastic processes --- Processus stochastiques --- Probabilities --- Random variables --- Characteristic functions --- Probabilités --- Variables aléatoires --- Fonctions caractéristiques --- Loi des grands nombres --- Law of large numbers
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Probability theory --- Probabilities --- Probabilités --- Problems, exercises, etc. --- Problèmes et exercices --- Problems, exercises, etc --- 519.213 --- -Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Probability distributions and densities. Normal distribution. Characteristic functions. Measures of dependence. Infinitely divisible laws. Stable laws --- -Probability distributions and densities. Normal distribution. Characteristic functions. Measures of dependence. Infinitely divisible laws. Stable laws --- 519.213 Probability distributions and densities. Normal distribution. Characteristic functions. Measures of dependence. Infinitely divisible laws. Stable laws --- -519.213 Probability distributions and densities. Normal distribution. Characteristic functions. Measures of dependence. Infinitely divisible laws. Stable laws --- Probability --- Probabilités --- Problèmes et exercices --- Probabilités. --- Probabilities - Problems, exercises, etc
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Stochastic processes --- Distribution (Probability theory) --- Distribution (Théorie des probabilités) --- 51 --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Mathematics --- 51 Mathematics --- Distribution (Théorie des probabilités)
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Extreme environmental events, such as floods, droughts, rainstorms, and high winds, have severe consequences for human society. How frequently an event of a given magnitude may be expected to occur is of great importance. Planning for weather-related emergencies, design of civil engineering structures, reservoir management, pollution control, and insurance risk calculations, all rely on knowledge of the frequency of these extreme events. Estimation of these frequencies is difficult because extreme events are by definition rare and the data record is often short. Regional frequency analysis resolves this problem by "trading space for time"; data from several sites are used in estimating event frequencies at any one site. L-moments are a recent development within statistics. They form the basis of an elegant mathematical theory in their own right and can be used to facilitate the estimation process in regional frequency analysis. L-moments methods are demonstrably superior to those that have been used previously and are now being adopted by many organizations worldwide. This book is the first complete account of the L-moment approach to regional frequency analysis. It brings together results that previously were scattered among academic journals and also includes much new material. Regional Frequency Analysis comprehensively describes the theoretical background to the subject, is rich in practical advice for users, and contains detailed examples that illustrate the approach. This book will be of great value to hydrologists, atmospheric scientists, and civil engineers concerned with environmental extremes.
Distribution (Probability theory) --- Natural disasters --- Natural calamities --- Disasters --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Forecasting --- Statistical methods. --- Forecasting&delete& --- Statistical methods
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