Hello
I was wondering if anyone has seen proofs of the following. Let
X=min(X_1,X_2) where X_1 and X_2 are bivariate normal. The mgf of X is in
"The American Statistician" May 1994 (Vol 48,2). Let \mu_1, \mu_2,
\sigma_1, \sigma_2, \rho represent the means, standard deviations, and
correlation coefficient of X_1 and X_2. It seems rather intuitive to me
that \frac{\partial E[X]}{\partial \mu_1} > 0, \frac{\partial
E[X]}{\partial \sigma_1} < 0 and \frac{\partial Var[X]}{\partial \sigma_1}
> 0 but I am having difficulty proving these. Numerical simulations
suggest that my intuition is right. Has anyone seen any proofs of these
anywhere.
In advance, thanks for your assistance.
Alan
Alan Ker
Department of Agricultural and Resource Economics,
University of Arizona,
Tucson, Az 85721-0023
ph (520) 621-6265
fax (520) 621-6250
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|