By Jurii V. Linnik, Iosif V. Ostrovskii
ISBN-10: 0821815989
ISBN-13: 9780821815984
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Extra info for Decomposition of Random Variables and Vectors
Example text
5) implies the existence of nk(F). Now suppose that m k(F) exists. 6). 'D is that if the moment mk(F), k ;;;ii 1, exists, then Wp(x) = o(x-k), x - + oo. § 2. Analyticity conditions for characteristic functions Let G be a region of the complex t-plane whose closure contains some real neighborhood r of the point t = 0. We shall assume that r is either int~rior to G or on its boundary; in the latter case, we stipulate that r contains no points of accumulation of nonreal points of the boundary of G.
5) ( rextF == P- 0 1 -oo We have SUFFICIENCY. 00 J (eitx_1- 1 ~x2 ) In ip(t, F) =iPt+ 1 ~/1 dG(x), -oo
With lext F = - oo. Suppose now that 0 Decomposition of Random Variables and Vectors by Jurii V. Linnik, Iosif V. Ostrovskii
by Paul
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