Abstract
Two general multivariate distributions in a real separable Hilbert space H are introduced in this article, one is multivariate Weibull distribution (denoted by GMWH), the other is multivariate Pareto distribution (denoted by GMPH). They are more general than the existing references. Some characterization theorems of the GMWH and GMPH via an intensively monotone operator are proved. The limiting behaviors and the interrelationship between the GMW and GMP in Euclidean space are also studied.
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