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Location change in marginal distributions of linear functions of random vectors
Authors:JK Ghosh  PK Ghosh
Institution:1. Indian Statistical Institute, India;1. University of Maryland, USA;2. Federal City College, Washington, D.C., USA
Abstract:Suppose X and Y are n × 1 random vectors such that lX + f(l) and lY have the same marginal distribution for all n × 1 real vectors l and some real valued function f(l), and the existence of expectations of X and Y is not necessary. Under these conditions it is proven that there exists a vector M such that f(l) = lM and X + M and Y have the same joint distribution. This result is extended to Banach-space valued random vectors.
Keywords:62H10  symmetrical distribution  “wrapping up” technique  characteristic functional  weak star topology  reflexive  separable  strong dual
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