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The Multivariate Normal Distribution

Technometrics, 1991
Contents: Introduction.- The Bivariate Normal Distribution.- Fundamental Properties and Sampling Distributions of the Multivariate Normal Distribution.- Other Related Properties.- Positively Dependent and Exchangeable Normal Variables.- Order Statistics of Normal Variables.- Related Inequalities.- Statistical Computing Related to the Multivariate ...
Alan Julian Izenman, Y. L. Tong
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Concentration inequalities for multivariate distributions: I. multivariate normal distributions

Statistics & Probability Letters, 1991
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Eaton, Morris L., Perlman, Michael D.
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On a characterization of multivariate normal distribution

Communications in Statistics, 1974
Khatri and Rao's theorem on a characterization of multivariate normal distribution through independence of linear functions of random vectors is extended to independence of more general functions satisfying an associativity equation.
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The multivariate complex normal distribution-a generalization

IEEE Transactions on Information Theory, 1995
Summary: The multivariate complex normal distribution usually employed in the literature is a special case since certain restrictions have been imposed on the covariances of the real and imaginary parts of its variables. A more general distribution is proposed of which the usual distribution is shown to be a special case.
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Multivariate Normal Distribution

2009
In this chapter, we define univariate and multivariate normal distribution density functions and then we discuss tests of differences of means for multiple variables simultaneously across groups.
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The Multivariate Normal Distribution

1997
Before introducing the multivariate normal distribution, let us briefly review some important results about the univariate normal.
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The multivariate normal distribution

1980
The multivariate normal distribution was briefly introduced in Chapter 2. In this chapter we consider its properties in some detail since the estimation of its parameters is the source of many standard multivariate statistical methods. In addition, we shall meet a number of derived distributions of fundamental importance.
Christopher Chatfield, Alexander J. Collins   +1 more
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Multivariate Normal Distributions

2011
The goal of this book is multidimensional: a) to help reviving Statistics education in many parts in the world where it is in crisis. For the first time authors from many developing countries have an opportunity to write together with the most prominent world authorities. The editor has spent several years searching for the most reputable statisticians
Hlupić, Nikica, Kalpić, Damir
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The Multivariate Normal Distribution

1995
In Chapter 1 we studied how to handle (linear transformations of) random vectors, that is, vectors whose components are random variables. Since the normal distribution is (one of) the most important distribution(s) and since there are special properties, methods, and devices pertaining to this distribution, we devote this chapter to the study of the ...
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Multivariate Normal Distribution

2015
IN THIS CHAPTER, we generalize the bivariate normal distribution from the previous chapter to an arbitrary number of dimensions. We also make use of the matrix notation. The mathematics is generally more dense and relies on the linear algebra notation covered in Chap. 4 In Sect. 4.5 we pointed out there is a limit on what computations we can reasonably
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