TY - JOUR
T1 - On the distribution of the maximum of bivariate normal random variables with general means and variances
AU - Kella, Offer
PY - 1986/1/1
Y1 - 1986/1/1
N2 - A great amount of effort has been devoted to achieving exact expressions for moments of order statistics of independent normal random variables, as well as the dependent case with the same correlation coefficients, means and variances. It does not seem as if there are handy formulae for the order statistics of even the simple bivariate normal random variables when the means and variances are allowed to be different. In this paper we give an explicit formula for the Laplace-Stieltjes Transform of the maximum of bivariate normal random variables by which we obtain formulae for the first two moments in the standard way.
AB - A great amount of effort has been devoted to achieving exact expressions for moments of order statistics of independent normal random variables, as well as the dependent case with the same correlation coefficients, means and variances. It does not seem as if there are handy formulae for the order statistics of even the simple bivariate normal random variables when the means and variances are allowed to be different. In this paper we give an explicit formula for the Laplace-Stieltjes Transform of the maximum of bivariate normal random variables by which we obtain formulae for the first two moments in the standard way.
KW - bivariate normal
KW - laplace-Stieltjes transform
KW - order statistics
UR - http://www.scopus.com/inward/record.url?scp=0007175313&partnerID=8YFLogxK
U2 - 10.1080/03610928608829308
DO - 10.1080/03610928608829308
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AN - SCOPUS:0007175313
SN - 0361-0926
VL - 15
SP - 3265
EP - 3276
JO - Communications in Statistics - Theory and Methods
JF - Communications in Statistics - Theory and Methods
IS - 11
ER -