• Mathematics

Multivariate Probability


Author: John McColl
Publisher: Wiley
ISBN: 9780340719961
Category: Mathematics
Page: 288
View: 1294
This book is a comprehensive guide to multivariate probability for students who have an elementary knowledge of probability and are ready to move on to more advanced concepts Topics covered include: A review of basic probability theory, including core ideas about random variables Bivariate distributions and the general theory of random vectors Relationships between random variables Normal linear model and multivariate sampling distributions Generating functions and convergence. Each section is illustrated with numerous examples. Multivariate probability deliberately avoids a measure-theoretic approach in order to make these complex concepts easily accessible to a broad readership. Attention is restricted to discrete and (absolutely) continuous random variables. Although proofs are given of all the main results, this book is primarily intended to provide readers with the tools they require to build appropriate probability models for real-life situations. The usefulness of simulation in this respect is emphasized throughout the book.

    • Mathematics

Decomposition of Multivariate Probabilities


Author: Roger Cuppens
Publisher: Academic Press
ISBN: 1483217647
Category: Mathematics
Page: 262
View: 2817
Decomposition of Multivariate Probability is a nine-chapter text that focuses on the problem of multivariate characteristic functions. After a brief introduction to some useful results on measures and integrals, this book goes on dealing with the classical theory and the Fourier-Stieltjes transforms of signed measures. The succeeding chapters explore the multivariate extension of the well-known Paley-Wiener theorem on functions that are entire of exponential type and square-integrable; the theory of infinitely divisible probabilities and the classical results of Hin?in; and the decompositions of analytic characteristic functions. Other chapters are devoted to the important problem of the description of a specific class on n-variate probabilities without indecomposable factors. The final chapter studies the problem of ?-decomposition of multivariate characteristic functions. This book will prove useful to mathematicians and advance undergraduate and graduate students.

    • Business & Economics

Copulae and Multivariate Probability Distributions in Finance


Author: Alexandra Dias,Mark Salmon,Chris Adcock
Publisher: Routledge
ISBN: 1317976916
Category: Business & Economics
Page: 208
View: 2288
Portfolio theory and much of asset pricing, as well as many empirical applications, depend on the use of multivariate probability distributions to describe asset returns. Traditionally, this has meant the multivariate normal (or Gaussian) distribution. More recently, theoretical and empirical work in financial economics has employed the multivariate Student (and other) distributions which are members of the elliptically symmetric class. There is also a growing body of work which is based on skew-elliptical distributions. These probability models all exhibit the property that the marginal distributions differ only by location and scale parameters or are restrictive in other respects. Very often, such models are not supported by the empirical evidence that the marginal distributions of asset returns can differ markedly. Copula theory is a branch of statistics which provides powerful methods to overcome these shortcomings. This book provides a synthesis of the latest research in the area of copulae as applied to finance and related subjects such as insurance. Multivariate non-Gaussian dependence is a fact of life for many problems in financial econometrics. This book describes the state of the art in tools required to deal with these observed features of financial data. This book was originally published as a special issue of the European Journal of Finance.

    • Mathematics

Probability Inequalities in Multivariate Distributions


Author: Y. L. Tong
Publisher: Academic Press
ISBN: 1483269213
Category: Mathematics
Page: 255
View: 5770
Probability Inequalities in Multivariate Distributions is a comprehensive treatment of probability inequalities in multivariate distributions, balancing the treatment between theory and applications. The book is concerned only with those inequalities that are of types T1-T5. The conditions for such inequalities range from very specific to very general. Comprised of eight chapters, this volume begins by presenting a classification of probability inequalities, followed by a discussion on inequalities for multivariate normal distribution as well as their dependence on correlation coefficients. The reader is then introduced to inequalities for other well-known distributions, including the multivariate distributions of t, chi-square, and F; inequalities for a class of symmetric unimodal distributions and for a certain class of random variables that are positively dependent by association or by mixture; and inequalities obtainable through the mathematical tool of majorization and weak majorization. The book also describes some distribution-free inequalities before concluding with an overview of their applications in simultaneous confidence regions, hypothesis testing, multiple decision problems, and reliability and life testing. This monograph is intended for mathematicians, statisticians, students, and those who are primarily interested in inequalities.

    • Computers

Computation of Multivariate Normal and t Probabilities


Author: Alan Genz,Frank Bretz
Publisher: Springer Science & Business Media
ISBN: 3642016898
Category: Computers
Page: 126
View: 4242
Multivariate normal and t probabilities are needed for statistical inference in many applications. Modern statistical computation packages provide functions for the computation of these probabilities for problems with one or two variables. This book describes recently developed methods for accurate and efficient computation of the required probability values for problems with two or more variables. The book discusses methods for specialized problems as well as methods for general problems. The book includes examples that illustrate the probability computations for a variety of applications.

    • Mathematics

Multivariate Statistics and Probability

Essays in Memory of Paruchuri R. Krishnaiah
Author: C. R. Rao,M. M. Rao
Publisher: Academic Press
ISBN: 1483263835
Category: Mathematics
Page: 582
View: 4657
Multivariate Statistics and Probability: Essays in Memory of Paruchuri R. Krishnaiah is a collection of essays on multivariate statistics and probability in memory of Paruchuri R. Krishnaiah (1932-1987), who made significant contributions to the fields of multivariate statistical analysis and stochastic theory. The papers cover the main areas of multivariate statistical theory and its applications, as well as aspects of probability and stochastic analysis. Topics range from finite sampling and asymptotic results, including aspects of decision theory, Bayesian analysis, classical estimation, regression, and time-series problems. Comprised of 35 chapters, this book begins with a discussion on the joint asymptotic distribution of marginal quantiles and quantile functions in samples from a multivariate population. The reader is then introduced to kernel estimators of density function of directional data; moment conditions for valid formal edgeworth expansions; and ergodicity and central limit theorems for a class of Markov processes. Subsequent chapters focus on minimal complete classes of invariant tests for equality of normal covariance matrices and sphericity; normed likelihood as saddlepoint approximation; generalized Gaussian random fields; and smoothness properties of the conditional expectation in finitely additive white noise filtering. This monograph should be of considerable interest to researchers as well as to graduate students working in theoretical and applied statistics, multivariate analysis, and random processes.

    • Mathematics

Methods of Multivariate Analysis


Author: Alvin C. Rencher,William F. Christensen
Publisher: John Wiley & Sons
ISBN: 1118391675
Category: Mathematics
Page: 800
View: 4832
Praise for the Second Edition "This book is a systematic, well-written, well-organized text on multivariate analysis packed with intuition and insight . . . There is much practical wisdom in this book that is hard to find elsewhere." —IIE Transactions Filled with new and timely content, Methods of Multivariate Analysis, Third Edition provides examples and exercises based on more than sixty real data sets from a wide variety of scientific fields. It takes a "methods" approach to the subject, placing an emphasis on how students and practitioners can employ multivariate analysis in real-life situations. This Third Edition continues to explore the key descriptive and inferential procedures that result from multivariate analysis. Following a brief overview of the topic, the book goes on to review the fundamentals of matrix algebra, sampling from multivariate populations, and the extension of common univariate statistical procedures (including t-tests, analysis of variance, and multiple regression) to analogous multivariate techniques that involve several dependent variables. The latter half of the book describes statistical tools that are uniquely multivariate in nature, including procedures for discriminating among groups, characterizing low-dimensional latent structure in high-dimensional data, identifying clusters in data, and graphically illustrating relationships in low-dimensional space. In addition, the authors explore a wealth of newly added topics, including: Confirmatory Factor Analysis Classification Trees Dynamic Graphics Transformations to Normality Prediction for Multivariate Multiple Regression Kronecker Products and Vec Notation New exercises have been added throughout the book, allowing readers to test their comprehension of the presented material. Detailed appendices provide partial solutions as well as supplemental tables, and an accompanying FTP site features the book's data sets and related SAS® code. Requiring only a basic background in statistics, Methods of Multivariate Analysis, Third Edition is an excellent book for courses on multivariate analysis and applied statistics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for both statisticians and researchers across a wide variety of disciplines.

    • Mathematics

Analysis of Incomplete Multivariate Data


Author: J.L. Schafer
Publisher: CRC Press
ISBN: 9781439821862
Category: Mathematics
Page: 448
View: 8562
The last two decades have seen enormous developments in statistical methods for incomplete data. The EM algorithm and its extensions, multiple imputation, and Markov Chain Monte Carlo provide a set of flexible and reliable tools from inference in large classes of missing-data problems. Yet, in practical terms, those developments have had surprisingly little impact on the way most data analysts handle missing values on a routine basis. Analysis of Incomplete Multivariate Data helps bridge the gap between theory and practice, making these missing-data tools accessible to a broad audience. It presents a unified, Bayesian approach to the analysis of incomplete multivariate data, covering datasets in which the variables are continuous, categorical, or both. The focus is applied, where necessary, to help readers thoroughly understand the statistical properties of those methods, and the behavior of the accompanying algorithms. All techniques are illustrated with real data examples, with extended discussion and practical advice. All of the algorithms described in this book have been implemented by the author for general use in the statistical languages S and S Plus. The software is available free of charge on the Internet.

Encyclopedia of Optimization


Author: N.A
Publisher: Springer Science & Business Media
ISBN: 0792369327
Category:
Page: 258
View: 1163

    • Mathematics

Probability Inequalities in Multivariate Distributions


Author: Y. L. Tong
Publisher: Academic Press
ISBN: 1483269213
Category: Mathematics
Page: 255
View: 8058
Probability Inequalities in Multivariate Distributions is a comprehensive treatment of probability inequalities in multivariate distributions, balancing the treatment between theory and applications. The book is concerned only with those inequalities that are of types T1-T5. The conditions for such inequalities range from very specific to very general. Comprised of eight chapters, this volume begins by presenting a classification of probability inequalities, followed by a discussion on inequalities for multivariate normal distribution as well as their dependence on correlation coefficients. The reader is then introduced to inequalities for other well-known distributions, including the multivariate distributions of t, chi-square, and F; inequalities for a class of symmetric unimodal distributions and for a certain class of random variables that are positively dependent by association or by mixture; and inequalities obtainable through the mathematical tool of majorization and weak majorization. The book also describes some distribution-free inequalities before concluding with an overview of their applications in simultaneous confidence regions, hypothesis testing, multiple decision problems, and reliability and life testing. This monograph is intended for mathematicians, statisticians, students, and those who are primarily interested in inequalities.

    • Mathematics

Multivariate Statistical Simulation

A Guide to Selecting and Generating Continuous Multivariate Distributions
Author: Mark E. Johnson
Publisher: John Wiley & Sons
ISBN: 1118150732
Category: Mathematics
Page: 240
View: 8860
Provides state-of-the-art coverage for the researcher confronted with designing and executing a simulation study using continuous multivariate distributions. Concise writing style makes the book accessible to a wide audience. Well-known multivariate distributions are described, emphasizing a few representative cases from each distribution. Coverage includes Pearson Types II and VII elliptically contoured distributions, Khintchine distributions, and the unifying class for the Burr, Pareto, and logistic distributions. Extensively illustrated--the figures are unique, attractive, and reveal very nicely what distributions ``look like.'' Contains an extensive and up-to-date bibliography culled from journals in statistics, operations research, mathematics, and computer science.

    • Business & Economics

High-Dimensional Probability

An Introduction with Applications in Data Science
Author: Roman Vershynin
Publisher: Cambridge University Press
ISBN: 1108415199
Category: Business & Economics
Page: 296
View: 6917
An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

    • Mathematics

Multivariate Models and Multivariate Dependence Concepts


Author: Harry Joe
Publisher: CRC Press
ISBN: 9780412073311
Category: Mathematics
Page: 424
View: 2548
This book on multivariate models, statistical inference, and data analysis contains deep coverage of multivariate non-normal distributions for modeling of binary, count, ordinal, and extreme value response data. It is virtually self-contained, and includes many exercises and unsolved problems.

    • Multivariate analysis

Probability Integrals of Multivariate Normal and Multivariate T


Author: Shanti Swarup Gupta
Publisher: N.A
ISBN: N.A
Category: Multivariate analysis
Page: 95
View: 2091
This paper gives a survey of the work on multivariate probability integral and related functions starting with the bivariate case and includes the author's recent work on the probability integrals of the multivariate normal and a multivariate analogue of Student's t. An annotated bibliography on evaluation of multivariate normal and t probability integrals (189 entries) is included. (Author).

    • Mathematics

Methods for Statistical Data Analysis of Multivariate Observations


Author: R. Gnanadesikan
Publisher: John Wiley & Sons
ISBN: 1118030923
Category: Mathematics
Page: 384
View: 1859
A practical guide for multivariate statistical techniques-- now updated and revised In recent years, innovations in computer technology and statistical methodologies have dramatically altered the landscape of multivariate data analysis. This new edition of Methods for Statistical Data Analysis of Multivariate Observations explores current multivariate concepts and techniques while retaining the same practical focus of its predecessor. It integrates methods and data-based interpretations relevant to multivariate analysis in a way that addresses real-world problems arising in many areas of interest. Greatly revised and updated, this Second Edition provides helpful examples, graphical orientation, numerous illustrations, and an appendix detailing statistical software, including the S (or Splus) and SAS systems. It also offers * An expanded chapter on cluster analysis that covers advances in pattern recognition * New sections on inputs to clustering algorithms and aids for interpreting the results of cluster analysis * An exploration of some new techniques of summarization and exposure * New graphical methods for assessing the separations among the eigenvalues of a correlation matrix and for comparing sets of eigenvectors * Knowledge gained from advances in robust estimation and distributional models that are slightly broader than the multivariate normal This Second Edition is invaluable for graduate students, applied statisticians, engineers, and scientists wishing to use multivariate techniques in a variety of disciplines.

    • Business & Economics

Probability and Statistics for Economists


Author: N.A
Publisher: World Scientific Publishing Company
ISBN: 9813228830
Category: Business & Economics
Page: 592
View: 5528
Probability and Statistics have been widely used in various fields of science, including economics. Like advanced calculus and linear algebra, probability and statistics are indispensable mathematical tools in economics. Statistical inference in economics, namely econometric analysis, plays a crucial methodological role in modern economics, particularly in empirical studies in economics. This textbook covers probability theory and statistical theory in a coherent framework that will be useful in graduate studies in economics, statistics and related fields. As a most important feature, this textbook emphasizes intuition, explanations and applications of probability and statistics from an economic perspective. Request Inspection Copy

    • Mathematics

Asymptotics in Statistics and Probability

Papers in Honor of George Gregory Roussas
Author: Madan L. Puri
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110942003
Category: Mathematics
Page: 453
View: 9581

    • Computers

Computation of Multivariate Normal and t Probabilities


Author: Alan Genz,Frank Bretz
Publisher: Springer Science & Business Media
ISBN: 3642016898
Category: Computers
Page: 126
View: 6938
Multivariate normal and t probabilities are needed for statistical inference in many applications. Modern statistical computation packages provide functions for the computation of these probabilities for problems with one or two variables. This book describes recently developed methods for accurate and efficient computation of the required probability values for problems with two or more variables. The book discusses methods for specialized problems as well as methods for general problems. The book includes examples that illustrate the probability computations for a variety of applications.

    • Mathematics

Symmetric Multivariate and Related Distributions


Author: Kai Wang Fang
Publisher: CRC Press
ISBN: 1351093940
Category: Mathematics
Page: 230
View: 1099
Since the publication of the by now classical Johnson and Kotz Continuous Multivariate Distributions (Wiley, 1972) there have been substantial developments in multivariate distribution theory especially in the area of non-normal symmetric multivariate distributions. The book by Fang, Kotz and Ng summarizes these developments in a manner which is accessible to a reader with only limited background (advanced real-analysis calculus, linear algebra and elementary matrix calculus). Many of the results in this field are due to Kai-Tai Fang and his associates and appeared in Chinese publications only. A thorough literature search was conducted and the book represents the latest work - as of 1988 - in this rapidly developing field of multivariate distributions. The authors are experts in statistical distribution theory.

    • Mathematics

Multivariate Dependencies

Models, Analysis and Interpretation
Author: D.R. Cox,Nanny Wermuth
Publisher: CRC Press
ISBN: 9780412754104
Category: Mathematics
Page: 272
View: 4685
Large observational studies involving research questions that require the measurement of several features on each individual arise in many fields including the social and medical sciences. This book sets out both the general concepts and the more technical statistical issues involved in analysis and interpretation. Numerous illustrative examples are described in outline and four studies are discussed in some detail. The use of graphical representations of dependencies and independencies among the features under study is stressed, both to incorporate available knowledge at the planning stage of an analysis and to summarize aspects important for interpretation after detailed statistical analysis is complete. This book is aimed at research workers using statistical methods as well as statisticians involved in empirical research.