Results 161 to 170 of about 2,765,689 (216)

Total Positivity Properties of Generalized Hypergeometric Functions of Matrix Argument [PDF]

Journal of Statistical Physics, 2004
In multivariate statistical analysis, several authors have studied the total positivity properties of the generalized (0F1) 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 0F1 functions fail to satisfy certain pairwise total positivity
Donald St. P. Richards
semanticscholar   +3 more sources

Series Expansion for a Hypergeometric Function of Matrix Argument with Applications

Australian Journal of Statistics, 1982
SummaryA series expansion is obtained for the confluent hypergeometric function of the second kind when the argument is a 2 times 2 positive definite matrix. Applications are made to the distributions of Hotelling's generalized T02 statistic, and the smallest latent root of the covariance matrix.
Rameshwar D. Gupta, Donald St. P. Richards   +1 more
semanticscholar   +4 more sources

Hypergeometric Functions of Scalar Matrix Argument are Expressible in Terms of Classical Hypergeometric Functions

SIAM Journal on Mathematical Analysis, 1985
It is shown that the hypergeometric function of $m \times m$ scalar matrix argument (cf. Herz, Annals of Math., 61 (1955), pp. 474–523) may be expressed as the Pfaffian of a matrix whose entries are evaluated in terms of classical hypergeometric functions. Applications, in multivariate statistical theory, are made to the distributions of eigenvalues of
Rameshwar D. Gupta, Donald St. P. Richards   +1 more
semanticscholar   +4 more sources

System of Partial Differential Equations for the Hypergeometric Function 1F1 of a Matrix Argument on Diagonal Regions

Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, 2016
The hypergeometric function 1F1 of a matrix argument Y is a symmetric entire function in the eigenvalues y1,...,ym of Y. It appears in the distribution function of the largest eigenvalue of a Wishart matrix and its numerical evaluation is important in multivariate distribution theory. Hashiguchi et al. (J.
Masayuki Noro
semanticscholar   +4 more sources

On the holonomic systems for the Gauss hypergeometric function and its confluent family of a matrix argument

Istanbul Journal of Mathematics
We investigate the several special functions defined by a matrix integral on the Hermitian matrix space of size n. They are the matrix argument analogues of the Gauss hypergeometric, Kummer’s confluent hypergeometric, the Bessel, the Hermite-Weber and Airy functions which play important roles in the multivariate statistical analysis and the random ...
Hironobu Kimura
semanticscholar   +4 more sources

Appell's hypergeometric functions of matrix arguments

Integral Transforms and Special Functions, 2016
ABSTRACTAppell's hypergeometric functions F1, F2 and F3 of matrix arguments are defined and their properties are studied. Applications to distribution theory are described in a technical report due to the authors.
Saralees Nadarajah, Daya K. Nagar
openaire   +3 more sources

Partial differential equations for hypergeometric functions ₃F₂ of matrix argument

Canadian Journal of Statistics, 1975
AbstractMany multivariate non‐null distributions and moment formulas can be expressed in terms of hypergeometric functions pFq of matrix arqument. Muirhead [6] and Constantine and Muirhead [2] gave partial differential equations for the functions of 2F1 of one argument matrix and two argument matrices, respectively.
Yasunori Fujikoshi
openaire   +3 more sources

On the integral representations of some of the Horn's double and Srivastava's triple hypergeometric functions of matrix arguments

Bulletin of Pure & Applied Sciences- Mathematics and Statistics, 2020
We propose to define the Horn's double hypergeometric functions H3 and H4 of matrix arguments and deduce some integral representations for these two functions. Utilizing the first author's definitions (Upadhyaya, Lalit Mohan and Dhami, H.S., Matrix generalizations of multiple hypergeometric functions; #1818, Nov.2001, IMA Preprint Series, University of
Lalit Mohan Upadhyaya, A. Kamal, Ayman Shehata   +2 more
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Asymptotic expansions of some matrix argument hypergeometric functions, with applications to macromolecules

Annals of the Institute of Statistical Mathematics, 1993
We have studied the asymptotics of two special two-matrix hypergeometric functions. The validity of the asymptotic expressions for these functions is seen in several selected numerical comparisons between the exact and asymptotic results. These hypergeometric functions find applications in configuration statistics of macromolecules as well as ...
Gaoyuan Wei, Bruce E. Eichinger
openaire   +3 more sources

On Exton's Triple hypergeometric functions of matrix arguments-ii

Bulletin of Pure & Applied Sciences- Mathematics and Statistics, 2017
Lalit Mohan Upadhyaya
  +5 more sources