# Download Probability Inequalities in Multivariate Distributions (Probability and mathematical statistics) fb2

### by Y. L. Tong

**ISBN:**0126949506**Category:**Math & Science**Author:**Y. L. Tong**Subcategory:**Mathematics**Other formats:**lit azw mbr lrf**Language:**English**Publisher:**Academic Pr (December 1, 1980)**Pages:**244 pages**FB2 size:**1297 kb**EPUB size:**1249 kb**Rating:**4.4**Votes:**538

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 o. .

Probability Inequalities in Multivariate Distributions is a comprehensive treatment of probability inequalities in multivariate distributions, balancing the treatment between theory and applications. 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.

Start by marking Probability Inequalities in Multivariate Distributions .

Start by marking Probability Inequalities in Multivariate Distributions as Want to Read: Want to Read savin. ant to Read. He is a Fellow of the American Statistical Association, a Fellow of the Institute of Mathematical Statistics, Yung Liang Tong, a mathematical statistician, received a . degree from National Taiwan University in 1958 and a P. from the University of Minnesota in 1967. In addition to numerous articles, he has written four books in statistics and probability and two books on essays in Chinese.

Series: Probability and Mathematical Statistics . Paperback: 521 pages. It does not describe thoroughly the multivariate normal distribution theory that one find in the classic text of Anderson. Anderson takes a much more algebraic approach and concentrates heavily on multivariate normal theory. As with many other books on multivariate analysis, factor analysis and structural equation modelling are given little or no coverage even though they are important in applied problems. Specialized books like Harman and Bollen give a detailed treatment of factor analysis and structural equation models respectively.

The book also describes some distribution-free inequalities before concluding with an overview of their applications in simultaneous confidence regions . B. Inequalities for Multivariate Normal Distribution.

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. C. Inequalities for Multivariate t, Chi-Square, F, and Other Well-Known Distributions.

Summary Comprised of eight chapters, this volume begins by presenting a classification of probability inequalities. 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

Probability Inequalities in Multivariate Distributions.

Probability Inequalities in Multivariate Distributions. Also, the concept of distribution-free tolerance intervals is applied to estimate the range of an uncertain quantity and extract the information about its distribution.

Probability inequalities with exponential bounds are very central both in probability and statistics. In particular, such inequalities can be used in statistical (especially nonparametric) inference to provide rates of convergence for various estimates

Probability inequalities with exponential bounds are very central both in probability and statistics. In particular, such inequalities can be used in statistical (especially nonparametric) inference to provide rates of convergence for various estimates. In this paper, maximal inequalities and probability inequalities with exponential bounds are presented for various statistics including sums of . random variables, sums of independent but not necessarily identically distributed random variables, and U-statistics.

In: Probability, Statistics and Mathematics: Essays in Honor of Samuel Karlin, pp. 271–289, (T. W. Anderson, et a. ed., Academic Press, San . Probability Inequalities in Multivariate Distributions. Academic Press, New York. zbMATHGoogle Scholar., Academic Press, San Diego, C. oogle Scholar.

and Y. L. Tong, Probability inequalities in multivariate distributions. Sixth Berkeley Sympos.

More by J. H. Kemperman. 2. S. Das Gupta, M. Eaton, I. Olkin, M. D. Perlman, L. J. Savage and M. Sobel, Inequalities on the probability content of convex regions for elliptically contoured distributions, Proc. Statistics and Probability (Berkeley, Calif. 1970), vol. II, 1972, pp. 241-265. Zentralblatt MATH: 0253.

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