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Copulas (mathematical statistics) --- Stochastic models

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This tome provides the reader with a background on simulating copulas and multivariate distribution in general. It unifies the scattered literature on the simulation of various families of copulas as well as on different construction principles.

Stochastic processes --- Computer. Automation --- Copulas (Mathematical statistics) --- Stochastic models. --- Copules (Statistique mathématique) --- Modèles stochastiques

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Complex environmental and hydrological processes are characterized by more than one correlated random variable. These events are multivariate and their treatment requires multivariate frequency analysis. Traditional analysis methods are, however, too restrictive and do not apply in many cases. Recent years have therefore witnessed numerous applications of copulas to multivariate hydrologic frequency analyses. This book describes the basic concepts of copulas, and outlines current trends and developments in copula methodology and applications. It includes an accessible discussion of the methods alongside simple step-by-step sample calculations. Detailed case studies with real-world data are included, and are organized based on applications, such as flood frequency analysis and water quality analysis. Illustrating how to apply the copula method to multivariate frequency analysis, engineering design, and risk and uncertainty analysis, this book is ideal for researchers, professionals and graduate students in hydrology and water resources engineering.

Copulas (Mathematical statistics) --- Hydrology --- Water-supply engineering --- Water resources development --- Mathematics. --- Mathematical models.

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This book is a collaborative effort from three workshops held over the last three years, all involving principal contributors to the vine-copula methodology. Research and applications in vines have been growing rapidly and there is now a growing need to collate basic results, and standardize terminology and methods. Specifically, this handbook will trace historical developments, standardizing notation and terminology, summarize results on bivariate copulae, summarize results for regular vines, and give an overview of its applications. In addition, many of these results are new and not readily

Mathematical statistics --- Copulas (Mathematical statistics) --- Distribution (Probability theory) --- 519.5 --- Copulas (Mathematical statistics). --- Dependence (Statistics) --- Distribution functions --- Frequency distribution --- Dependence of random variables --- Random variables, Dependence of --- Stochastic dependence --- Characteristic functions --- Probabilities

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Copulas are functions that join multivariate distribution functions to their one-dimensional margins. The study of copulas and their role in statistics is a new but vigorously growing field. In this book the student or practitioner of statistics and probability will find discussions of the fundamental properties of copulas and some of their primary applications. The applications include the study of dependence and measures of association, and the construction of families of bivariate distributions. With nearly a hundred examples and over 150 exercises, this book is suitable as a text or for self-study. The only prerequisite is an upper level undergraduate course in probability and mathematical statistics, although some familiarity with nonparametric statistics would be useful. Knowledge of measure-theoretic probability is not required. Roger B. Nelsen is Professor of Mathematics at Lewis & Clark College in Portland, Oregon. He is also the author of "Proofs Without Words: Exercises in Visual Thinking," published by the Mathematical Association of America.

519.22 --- 519.22 Statistical theory. Statistical models. Mathematical statistics in general --- Statistical theory. Statistical models. Mathematical statistics in general --- Copulas (mathematical statistics) --- Copulas (Mathematical statistics) --- Copulas (Mathematical statistics). --- Distribution (Probability theory) --- Stochastic processes --- Mathematical statistics --- Statistics . --- Economics, Mathematical . --- Statistical Theory and Methods. --- Quantitative Finance. --- Economics --- Mathematical economics --- Econometrics --- Mathematics --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Methodology --- Statistique