The Methods Of Distances In The Theory Of Probability And Statistics

Author : Svetlozar T. Rachev,Lev Klebanov,Stoyan V. Stoyanov,Frank Fabozzi
Publisher : Springer Science & Business Media
Page : 616 pages
File Size : 52,5 Mb
Release : 2013-01-04
Category : Mathematics
ISBN : 9781461448693

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The Methods of Distances in the Theory of Probability and Statistics by Svetlozar T. Rachev,Lev Klebanov,Stoyan V. Stoyanov,Frank Fabozzi Pdf

This book covers the method of metric distances and its application in probability theory and other fields. The method is fundamental in the study of limit theorems and generally in assessing the quality of approximations to a given probabilistic model. The method of metric distances is developed to study stability problems and reduces to the selection of an ideal or the most appropriate metric for the problem under consideration and a comparison of probability metrics. After describing the basic structure of probability metrics and providing an analysis of the topologies in the space of probability measures generated by different types of probability metrics, the authors study stability problems by providing a characterization of the ideal metrics for a given problem and investigating the main relationships between different types of probability metrics. The presentation is provided in a general form, although specific cases are considered as they arise in the process of finding supplementary bounds or in applications to important special cases. Svetlozar T. Rachev is the Frey Family Foundation Chair of Quantitative Finance, Department of Applied Mathematics and Statistics, SUNY-Stony Brook and Chief Scientist of Finanlytica, USA. Lev B. Klebanov is a Professor in the Department of Probability and Mathematical Statistics, Charles University, Prague, Czech Republic. Stoyan V. Stoyanov is a Professor at EDHEC Business School and Head of Research, EDHEC-Risk Institute—Asia (Singapore). Frank J. Fabozzi is a Professor at EDHEC Business School. (USA)

Author : F.M. Dekking,C. Kraaikamp,H.P. Lopuhaä,L.E. Meester
Publisher : Springer Science & Business Media
Page : 488 pages
File Size : 52,6 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9781846281686

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A Modern Introduction to Probability and Statistics by F.M. Dekking,C. Kraaikamp,H.P. Lopuhaä,L.E. Meester Pdf

Suitable for self study Use real examples and real data sets that will be familiar to the audience Introduction to the bootstrap is included – this is a modern method missing in many other books

Author : Ayanendranath Basu,Hiroyuki Shioya,Chanseok Park
Publisher : CRC Press
Page : 424 pages
File Size : 55,7 Mb
Release : 2011-06-22
Category : Computers
ISBN : 9781420099669

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Statistical Inference by Ayanendranath Basu,Hiroyuki Shioya,Chanseok Park Pdf

In many ways, estimation by an appropriate minimum distance method is one of the most natural ideas in statistics. However, there are many different ways of constructing an appropriate distance between the data and the model: the scope of study referred to by "Minimum Distance Estimation" is literally huge. Filling a statistical resource gap, Stati

Author : Bert E. Fristedt,Lawrence F. Gray
Publisher : Springer Science & Business Media
Page : 775 pages
File Size : 46,7 Mb
Release : 2013-11-21
Category : Mathematics
ISBN : 9781489928375

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A Modern Approach to Probability Theory by Bert E. Fristedt,Lawrence F. Gray Pdf

Students and teachers of mathematics and related fields will find this book a comprehensive and modern approach to probability theory, providing the background and techniques to go from the beginning graduate level to the point of specialization in research areas of current interest. The book is designed for a two- or three-semester course, assuming only courses in undergraduate real analysis or rigorous advanced calculus, and some elementary linear algebra. A variety of applications—Bayesian statistics, financial mathematics, information theory, tomography, and signal processing—appear as threads to both enhance the understanding of the relevant mathematics and motivate students whose main interests are outside of pure areas.

Author : Paul W. Jr. Mielke,Kenneth J. Berry
Publisher : Springer Science & Business Media
Page : 359 pages
File Size : 49,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475734492

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Permutation Methods by Paul W. Jr. Mielke,Kenneth J. Berry Pdf

The book provides a comprehensive treatment of statistical inference using permutation techniques. It features a variety of useful and powerful data analytic tools that rely on very few distributional assumptions. Although many of these procedures have appeared in journal articles, they are not readily available to practitioners.

Author : Friedrich Liese,Igor Vajda
Publisher : Unknown
Page : 228 pages
File Size : 40,5 Mb
Release : 1987
Category : Convex functions
ISBN : UCAL:B4405790

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Convex Statistical Distances by Friedrich Liese,Igor Vajda Pdf

Author : Vladimir I. Bogachev
Publisher : American Mathematical Soc.
Page : 286 pages
File Size : 51,7 Mb
Release : 2018-09-27
Category : Convergence
ISBN : 9781470447380

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Weak Convergence of Measures by Vladimir I. Bogachev Pdf

This book provides a thorough exposition of the main concepts and results related to various types of convergence of measures arising in measure theory, probability theory, functional analysis, partial differential equations, mathematical physics, and other theoretical and applied fields. Particular attention is given to weak convergence of measures. The principal material is oriented toward a broad circle of readers dealing with convergence in distribution of random variables and weak convergence of measures. The book contains the necessary background from measure theory and functional analysis. Large complementary sections aimed at researchers present the most important recent achievements. More than 100 exercises (ranging from easy introductory exercises to rather difficult problems for experienced readers) are given with hints, solutions, or references. Historic and bibliographic comments are included. The target readership includes mathematicians and physicists whose research is related to probability theory, mathematical statistics, functional analysis, and mathematical physics.

Author : Richard von Mises
Publisher : Academic Press
Page : 709 pages
File Size : 41,8 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483264028

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Mathematical Theory of Probability and Statistics by Richard von Mises Pdf

Mathematical Theory of Probability and Statistics focuses on the contributions and influence of Richard von Mises on the processes, methodologies, and approaches involved in the mathematical theory of probability and statistics. The publication first elaborates on fundamentals, general label space, and basic properties of distributions. Discussions focus on Gaussian distribution, Poisson distribution, mean value variance and other moments, non-countable label space, basic assumptions, operations, and distribution function. The text then ponders on examples of combined operations and summation of chance variables characteristic function. The book takes a look at the asymptotic distribution of the sum of chance variables and probability inference. Topics include inference from a finite number of observations, law of large numbers, asymptotic distributions, limit distribution of the sum of independent discrete random variables, probability of the sum of rare events, and probability density. The text also focuses on the introduction to the theory of statistical functions and multivariate statistics. The publication is a dependable source of information for researchers interested in the mathematical theory of probability and statistics

Author : Florence Nightingale David
Publisher : Unknown
Page : 230 pages
File Size : 40,9 Mb
Release : 1951
Category : Mathematical statistics
ISBN : OCLC:219845118

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Probability Theory for Statistical Methods by Florence Nightingale David Pdf

Author : S. T. Buckland,E.A. Rexstad,T.A. Marques,C.S. Oedekoven
Publisher : Springer
Page : 277 pages
File Size : 41,8 Mb
Release : 2015-08-08
Category : Medical
ISBN : 9783319192192

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Distance Sampling: Methods and Applications by S. T. Buckland,E.A. Rexstad,T.A. Marques,C.S. Oedekoven Pdf

In this book, the authors cover the basic methods and advances within distance sampling that are most valuable to practitioners and in ecology more broadly. This is the fourth book dedicated to distance sampling. In the decade since the last book published, there have been a number of new developments. The intervening years have also shown which advances are of most use. This self-contained book covers topics from the previous publications, while also including recent developments in method, software and application. Distance sampling refers to a suite of methods, including line and point transect sampling, in which animal density or abundance is estimated from a sample of distances to detected individuals. The book illustrates these methods through case studies; data sets and computer code are supplied to readers through the book’s accompanying website. Some of the case studies use the software Distance, while others use R code. The book is in three parts. The first part addresses basic methods, the design of surveys, distance sampling experiments, field methods and data issues. The second part develops a range of modelling approaches for distance sampling data. The third part describes variations in the basic method; discusses special issues that arise when sampling different taxa (songbirds, seabirds, cetaceans, primates, ungulates, butterflies, and plants); considers advances to deal with failures of the key assumptions; and provides a check-list for those conducting surveys.

Author : Harold J. Larson
Publisher : Unknown
Page : 408 pages
File Size : 40,8 Mb
Release : 1969
Category : Mathematics
ISBN : UOM:39015015712386

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Introduction to Probability Theory and Statistical Inference by Harold J. Larson Pdf

Author : Przemyslaw Grzegorzewski,Olgierd Hryniewicz,Maria A. Gil
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 45,5 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9783790817737

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Soft Methods in Probability, Statistics and Data Analysis by Przemyslaw Grzegorzewski,Olgierd Hryniewicz,Maria A. Gil Pdf

Classical probability theory and mathematical statistics appear sometimes too rigid for real life problems, especially while dealing with vague data or imprecise requirements. These problems have motivated many researchers to "soften" the classical theory. Some "softening" approaches utilize concepts and techniques developed in theories such as fuzzy sets theory, rough sets, possibility theory, theory of belief functions and imprecise probabilities, etc. Since interesting mathematical models and methods have been proposed in the frameworks of various theories, this text brings together experts representing different approaches used in soft probability, statistics and data analysis.

Author : Patrick Billingsley
Publisher : John Wiley & Sons
Page : 612 pages
File Size : 53,7 Mb
Release : 2017
Category : Electronic
ISBN : 8126517719

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Probability and Measure by Patrick Billingsley Pdf

Now in its new third edition, Probability and Measure offers advanced students, scientists, and engineers an integrated introduction to measure theory and probability. Retaining the unique approach of the previous editions, this text interweaves material on probability and measure, so that probability problems generate an interest in measure theory and measure theory is then developed and applied to probability. Probability and Measure provides thorough coverage of probability, measure, integration, random variables and expected values, convergence of distributions, derivatives and conditional probability, and stochastic processes. The Third Edition features an improved treatment of Brownian motion and the replacement of queuing theory with ergodic theory.· Probability· Measure· Integration· Random Variables and Expected Values· Convergence of Distributions· Derivatives and Conditional Probability· Stochastic Processes

Author : Christopher G. Small,Don L. McLeish
Publisher : John Wiley & Sons
Page : 268 pages
File Size : 51,6 Mb
Release : 2011-09-15
Category : Mathematics
ISBN : 9781118165539

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Hilbert Space Methods in Probability and Statistical Inference by Christopher G. Small,Don L. McLeish Pdf

Explains how Hilbert space techniques cross the boundaries into the foundations of probability and statistics. Focuses on the theory of martingales stochastic integration, interpolation and density estimation. Includes a copious amount of problems and examples.

Author : Victor M. Panaretos,Yoav Zemel
Publisher : Springer Nature
Page : 157 pages
File Size : 55,9 Mb
Release : 2020-03-10
Category : Mathematics
ISBN : 9783030384388

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An Invitation to Statistics in Wasserstein Space by Victor M. Panaretos,Yoav Zemel Pdf

This open access book presents the key aspects of statistics in Wasserstein spaces, i.e. statistics in the space of probability measures when endowed with the geometry of optimal transportation. Further to reviewing state-of-the-art aspects, it also provides an accessible introduction to the fundamentals of this current topic, as well as an overview that will serve as an invitation and catalyst for further research. Statistics in Wasserstein spaces represents an emerging topic in mathematical statistics, situated at the interface between functional data analysis (where the data are functions, thus lying in infinite dimensional Hilbert space) and non-Euclidean statistics (where the data satisfy nonlinear constraints, thus lying on non-Euclidean manifolds). The Wasserstein space provides the natural mathematical formalism to describe data collections that are best modeled as random measures on Euclidean space (e.g. images and point processes). Such random measures carry the infinite dimensional traits of functional data, but are intrinsically nonlinear due to positivity and integrability restrictions. Indeed, their dominating statistical variation arises through random deformations of an underlying template, a theme that is pursued in depth in this monograph.