Total positivity properties of generalized hypergeometric functions of matrix argument

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In multivariate statistical analysis, several authors have studied the total positivity properties of the generalized ( 0F 1) hypergeometric function of two real symmetric matrix arguments. In this paper, we make use of zonal polynomial expansions to obtain a new proof of a result that these 0F 1 functions fail to satisfy certain pairwise total positivity properties; this proof extends both to arbitrary generalized ( rF s) functions of two matrix arguments and to the generalized hypergeometric functions of Hermitian matrix arguments. In the case of the generalized hypergeometric functions of two Hermitian matrix arguments, we prove that these functions satisfy certain modified pairwise TP 2 properties; the proofs of these results are based on Sylvester's formula for compound determinants and the condensation formula of C. L. Dodgson [Lewis Carroll] (1866).

Original languageEnglish (US)
Pages (from-to)907-922
Number of pages16
JournalJournal of Statistical Physics
Volume116
Issue number1-4
DOIs
StatePublished - Aug 1 2004

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Total Positivity
Generalized Hypergeometric Function
hypergeometric functions
Hermitian matrix
matrices
multivariate statistical analysis
Pairwise
Zonal Polynomials
Multivariate Statistical Analysis
determinants
Hypergeometric Functions
polynomials
condensation
Condensation
Symmetric matrix
Determinant
expansion
Arbitrary

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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Total positivity properties of generalized hypergeometric functions of matrix argument. / Richards, Donald.

In: Journal of Statistical Physics, Vol. 116, No. 1-4, 01.08.2004, p. 907-922.

Research output: Contribution to journalArticle

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