Selfdecomposable distributions for maxima of independent random vectors

Summary In the present paper the limit laws for conveniently normalized multivariate sample extremes are characterized by means of the decomposability of probability distributions. Continuous automorphisms ofR^d =[–,]^d with respect to the operation v defined by x y=(max(x_i, y_i),i=1... d) are treated as norming mappings. An integral representation of the limit distributions is found using their log-concavity and a decomposition ofR^d in orbits of the norming family. Finally an example is given as an illustration.Research supported in part by the Committee of Science, Bulgarian Concil of Ministers, under contract no. 60/1987