scholarly journals Multivariate Distribution Theory

2013 ◽  
pp. 125-230
Keyword(s):  
Distribution Theory ◽  
Multivariate Distribution

scholarly journals On Multivariate Distribution Theory

1954 ◽  
Vol 25 (2) ◽  
pp. 329-339 ◽  
Author(s):  
I. Olkin ◽  
S. N. Roy
Keyword(s):  
Distribution Theory ◽  
Multivariate Distribution

Methods for Constructing Top Order Invariant Polynomials

1987 ◽  
Vol 3 (2) ◽  
pp. 195-207 ◽  
Author(s):  
Yasuko Chikuse
Keyword(s):  
Symmetric Matrix ◽  
Distribution Theory ◽  
Multivariate Distribution ◽  
Invariant Polynomials ◽  
Zonal Polynomials ◽  
Explicit Formulae ◽  
Order Invariant

The invariant polynomials (Davis [8] and Chikuse [2] with r(r ≥ 2) symmetric matrix arguments have been defined, extending the zonal polynomials, and applied in multivariate distribution theory. The usefulness of the polynomials has attracted the attention of econometricians, and some recent papers have applied the methods to distribution theory in econometrics (e.g., Hillier [14] and Phillips [22]).The ‘top order’ invariant polynomials , in which each of the partitions of ki 1 = 1,…,r, and has only one part, occur frequently in multivariate distribution theory (e.g., Hillier and Satchell [17] and Phillips [27]). In this paper we give three methods of constructing these polynomials, extending those of Ruben [28] for the top order zonal polynomials. The first two methods yield explicit formulae for the polynomials and then we give a recurrence procedure. It is shown that some of the expansions presented in Chikuse and Davis [4] are simplified for the top order invariant polynomials. A brief discussion is given on the ‘lowest order’ invariant polynomials.

A Survey on the Invariant Polynomials with Matrix Arguments in Relation to Econometric Distribution Theory

1986 ◽  
Vol 2 (2) ◽  
pp. 232-248 ◽  
Author(s):  
Yasuko Chikuse ◽  
A. W. Davis
Keyword(s):  
Power Series ◽  
Distribution Theory ◽  
Multivariate Distribution ◽  
Group Representations ◽  
Invariant Polynomials ◽  
Zonal Polynomials

Invariant polynomials with matrix arguments have been defined by the theory of group representations, generalizing the zonal polynomials. They have developed as a useful tool to evaluate certain integrals arising in multivariate distribution theory, which were expanded as power series in terms of the invariant polynomials. Some interest in the polynomials has been shown by people working in the field of econometric theory. In this paper, we shall survey the properties of the invariant polynomials and their applications in multivariate distribution theory including related developments in econometrics.

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