Continuous Bivariate Distributions

ISBN-13: 9780387096131 / Angielski / Twarda / 2009 / 724 str.

N. Balakrishnan; C. D. Lai

Opis

This volume, which is completely dedicated to continuous bivariate dist- butions, describes in detail their forms, properties, dependence structures, computation, and applications. It is a comprehensive and thorough revision ofanearliereditionof"ContinuousBivariateDistributions, Emphasizing- plications" by T.P. Hutchinson and C.D. Lai, published in 1990 by Rumsby Scienti?c Publishing, Adelaide, Australia. It has been nearly two decades since the publication of that book, and much has changed in this area of research during this period. Generali- tions have been considered for many known standard bivariate distributions. Skewed versions of di?erent bivariate distributions have been proposed and appliedtomodeldatawithskewnessdepartures.Byspecifyingthetwocon- tional distributions, rather than the simple speci?cation of one marginal and one conditional distribution, several general families of conditionally spe- ?ed bivariate distributions have been derived and studied at great length. Finally, bivariate distributions generated by a variety of copulas and their ?exibility (in terms of accommodating association/correlation) and str- tural properties have received considerable attention. All these developments andadvancesnecessitatedthepresentvolumeandhavethusresultedinas- stantially di?erent version than the last edition, both in terms of coverage and topics of discussion.

Recenzje

From the reviews of the second edition:

"The authors present the forms, properties, dependence structures, computation, and applications of numerous continuous bivariate distributions. ... One of the nice features of this edition is that it presents bivariate distributions that are generated by a variety of copulas. ... The new edition is comprised of 14 chapters including references at the end of each chapter ... and subject index at the end. ... I can safely recommend this book as a handy resource manual for researchers as well as practitioners working in this area." (Technometrics, Vol. 51 (4), November, 2009)

"The book begins with a survey of univariate distributions, necessary to clarify notation in subsequent chapters. ... Every time you open this volume, even at a random page, you'll likely find something of interest. ... You might well recommend it as collateral reading in a statistics class that you are teaching. As the students progress in their academic pursuits and/or in their subsequent careers, it will be a useful reference." (Barry C. Arnold, Mathematical Reviews, Issue 2012 h)

Spis treści

Univariate distributions. - Bivariate copulas. - Distributions expressed as copulas. - Concepts of stochastic dependence. - Measures of dependence. - Constructions of bivariate distributions.- Bivariate distributions constructed by conditional approach. - Variables in common method. - Bivariate gamma and related distributions. - Simple forms of the bivariate density function. - Bivariate exponentional and related distributions. - Bivariate normal distribution. - Bivariate extreme value distributions. - Elliptically symmetric bivariate distributions and other symmetric distributions. - Simulation of bivariate observations.

O autorze

N. BALAKRISHNAN, PhD, is Professor of Mathematics and Statistics at McMaster University in Hamilton, Ontario, Canada.V. B. NEVZOROV, PhD, DS, is Professor of Probability and Statistics at St. Petersburg State University in St. Petersburg, Russia.

Blurb

Random variables are rarely independent in practice and so many multivariate distributions have been proposed in the literature to give a dependence structure for two or more variables. In this book, we restrict ourselves to the bivariate distributions for two reasons: (i) correlation structure and other properties are easier to understand and the joint density plot can be displayed more easily, and (ii) a bivariate distribution can normally be extended to a multivariate one through a vector or matrix representation. This volume is a revision of Chapters 1-17 of the previous book Continuous Bivariate Distributions, Emphasising Applications authored by Drs. Paul Hutchinson and Chin-Diew Lai.

The book updates the subject of copulas which have grown immensely during the past two decades. Similarly, conditionally specified distributions and skewed distributions have become important topics of discussion in this area of research. This volume, which provides an up-to-date review of various developments relating to bivariate distributions in general, should be of interest to academics and graduate students, as well as applied researchers in finance, economics, science, engineering and technology.

N. BALAKRISHNAN is Professor in the Department of Mathematics and Statistics at McMaster University, Hamilton, Ontario, Canada. He has published numerous research articles in many areas of probability and statistics and has authored a number of books including the four-volume series on Distributions in Statistics, jointly with Norman L. Johnson and S. Kotz, published by Wiley. He is a Fellow of the American Statistical Association and the Institute of Mathematical Statistics, and the Editor-in-Chief of Communications in Statistics and the Executive Editor of Journal of Statistical Planning and Inference.

CHIN-DIEW LAI holds a Personal Chair in Statistics at Massey University, Palmerston North, New Zealand. He has published more than 100 peer-reviewed research articles and co-authored three well-received books. He was a former editor-in-chief and is now an Associate Editor of the Journal of Applied Mathematics and Decision Sciences.