  Kotlarski (1978) proved a result on identification of the distributions of
independent random variables $X,Y$ and $Z$ from the joint distribution of the
bivariate random vector $(U,V)$ where $(U,V)= (\max(X,Z),\max(Y,Z)).$ We extend
this result to the case $(U,V)=(\max(X,aZ_1,bZ_2),\max(Y,cZ_1,dZ_2))$ where
$X,Y,Z_1,Z_2$ are independent or max-independent random variables, $Z_1$ and
$Z_2$ are identically distributed and $a,b,c,d$ are known positive constants.
