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 Λ y=(max(x i, yi),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.
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Research supported in part by the Committee of Science, Bulgarian Concil of Ministers, under contract no. 60/1987
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Pancheva, E.I. Selfdecomposable distributions for maxima of independent random vectors. Probab. Th. Rel. Fields 84, 267–278 (1990). https://doi.org/10.1007/BF01197848
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DOI: https://doi.org/10.1007/BF01197848