TY - JOUR
T1 - Matrix Variate Distribution Theory under Elliptical Models—V
T2 - The Non-Central Wishart and Inverted Wishart Distributions
AU - Caro-Lopera, Francisco J.
AU - González Farías, Graciela
AU - Balakrishnan, N.
N1 - Funding Information:
This research work was supported by a joint project between the University of Medellin (Medellin, Colombia) and the Center for Mathematical Research (Guanajuato, Mexico). We are greatly thankful with the Editor and the Referees of this paper. Their carefully revisions and comments provided important improvement of the final version of this article.
Publisher Copyright:
© 2022, Allerton Press, Inc.
PY - 2022/3
Y1 - 2022/3
N2 - Abstract: The non-central Wishart and inverted Wishart distributions are studied in this work under elliptical models; some distributional results are based on some generalizations of the well-known Kummer relations, which leds us to determine that some moments have a polynomial representation. Then the non-central F and ‘‘studentized Wishart’’ distributions are derived in a general setting. After some generalizations, including the so called non-central generalized inverted Wishart distribution, the classical results based on Gaussian models are derived here as corollaries.
AB - Abstract: The non-central Wishart and inverted Wishart distributions are studied in this work under elliptical models; some distributional results are based on some generalizations of the well-known Kummer relations, which leds us to determine that some moments have a polynomial representation. Then the non-central F and ‘‘studentized Wishart’’ distributions are derived in a general setting. After some generalizations, including the so called non-central generalized inverted Wishart distribution, the classical results based on Gaussian models are derived here as corollaries.
KW - elliptical models
KW - F and ‘‘studentized Wishart’’ distributions
KW - generalized non-central Wishart
KW - inverted Wishart
KW - zonal and invariant polynomials
UR - http://www.scopus.com/inward/record.url?scp=85134371301&partnerID=8YFLogxK
U2 - 10.3103/S1066530722010021
DO - 10.3103/S1066530722010021
M3 - Artículo
AN - SCOPUS:85134371301
SN - 1066-5307
VL - 31
SP - 18
EP - 42
JO - Mathematical Methods of Statistics
JF - Mathematical Methods of Statistics
IS - 1
ER -