On a characterization of probability distribution based on maxima of independent or max-independent random variables
Abstract
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)= ((X,Z),(Y,Z)). We extend this result to the case (U,V)=((X,aZ1,bZ2),(Y,cZ1,dZ2)) where X,Y,Z1,Z2 are independent or max-independent random variables, Z1 and Z2 are identically distributed and a,b,c,d are known positive constants.
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