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Distribution (Probability theory)  Distribution functions  Frequency distribution  Characteristic functions  Probabilities
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Distribution (Probability theory)  Distribution functions  Frequency distribution  Characteristic functions  Probabilities
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"Interest in the skewnormal 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 (nonmeasuretheoretic) 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
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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 crosssection 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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Random matrix theory is a wide and growing field with a variety of concepts, results, and techniques and a vast range of applications in mathematics and the related sciences. This book offers beginners a fairly balanced collection of basic facts and methods.
Distribution (Probability theory)  Random matrices  Distribution functions  Frequency distribution  Characteristic functions  Probabilities  Matrices, Random  Matrices
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Concentration inequalities, which express the fact that certain complicated random variables are almost constant, have proven of utmost importance in many areas of probability and statistics. This volume contains refined versions of these inequalities, and their relationship to many applications particularly in stochastic analysis. The broad range and the high quality of the contributions make this book highly attractive for graduates, postgraduates and researchers in the above areas.
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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)  padic groups  Groups, padic  Group theory  Distribution functions  Frequency distribution  Characteristic functions  Probabilities
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This book is a readable, digestible introduction to exponential families, encompassing statistical models based on the most useful distributions in statistical theory, including the normal, gamma, binomial, Poisson, and negative binomial. Strongly motivated by applications, it presents the essential theory and then demonstrates the theory's practical potential by connecting it with developments in areas like item response analysis, social network models, conditional independence and latent variable structures, and point process models. Extensions to incomplete data models and generalized linear models are also included. In addition, the author gives a concise account of the philosophy of Per MartinLöf in order to connect statistical modelling with ideas in statistical physics, including Boltzmann's law. Written for graduate students and researchers with a background in basic statistical inference, the book includes a vast set of examples demonstrating models for applications and exercises embedded within the text as well as at the ends of chapters.
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