Total positivity properties of generalized hypergeometric functions of matrix argument

Research output: Contribution to journalArticle

3 Scopus citations

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

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Fingerprint Dive into the research topics of 'Total positivity properties of generalized hypergeometric functions of matrix argument'. Together they form a unique fingerprint.

  • Cite this