Continuous Bivariate Distributions: Second Edition

Chin Diew Lai, N. Balakrishnan (auth.)9780387096131, 0387096132, 9780387096148, 0387096140

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 ofApplied Mathematics and Decision Sciences.

Table of contents :
Front Matter….Pages i-xxxiv
Univariate Distributions….Pages 1-32
Bivariate Copulas….Pages 33-65
Distributions Expressed as Copulas….Pages 67-103
Concepts of Stochastic Dependence….Pages 105-140
Measures of Dependence….Pages 141-177
Construction of Bivariate Distributions….Pages 179-228
Bivariate Distributions Constructed by the Conditional Approach….Pages 229-278
Variables-in-Common Method….Pages 279-304
Bivariate Gamma and Related Distributions….Pages 305-350
Simple Forms of the Bivariate Density Function….Pages 351-400
Bivariate Exponential and Related Distributions….Pages 401-475
Bivariate Normal Distribution….Pages 477-561
Bivariate Extreme-Value Distributions….Pages 563-590
Elliptically Symmetric Bivariate Distributions and Other Symmetric Distributions….Pages 591-622
Simulation of Bivariate Observations….Pages 623-653
Back Matter….Pages 1-30