TY - JOUR
T1 - A Characterization of a Matric‐Variate Exponential Distribution
AU - Richards, Donald St P.
PY - 1981/6
Y1 - 1981/6
N2 - Suppose S is a positive definite m x m random matrix and S> Ω denotes the event that S—Ω is positive definite, Ω being a constant positive definite matrix. Under very mild regularity conditions, we show that the constraint Pr(S>Ω1+Ω2 | S>Ω2) = Pr(S>Ω1) implies that S has a Wishart distribution on m+ 1 degrees of freedom.
AB - Suppose S is a positive definite m x m random matrix and S> Ω denotes the event that S—Ω is positive definite, Ω being a constant positive definite matrix. Under very mild regularity conditions, we show that the constraint Pr(S>Ω1+Ω2 | S>Ω2) = Pr(S>Ω1) implies that S has a Wishart distribution on m+ 1 degrees of freedom.
UR - http://www.scopus.com/inward/record.url?scp=84985630963&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84985630963&partnerID=8YFLogxK
U2 - 10.1111/j.1467-842X.1981.tb00782.x
DO - 10.1111/j.1467-842X.1981.tb00782.x
M3 - Article
AN - SCOPUS:84985630963
SN - 0004-9581
VL - 23
SP - 238
EP - 239
JO - Australian Journal of Statistics
JF - Australian Journal of Statistics
IS - 2
ER -