The difference between the product and the convolution product of distribution functions in Rn | Zendy

Edward Omey | Zendy; Rein Vesilo | Zendy

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The difference between the product and the convolution product of distribution functions in Rn

Author(s) -

Edward Omey,

Rein Vesilo

Publication year - 2011

Publication title -

publications de l institut mathematique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.246

H-Index - 17

eISSN - 1820-7405

pISSN - 0350-1302

DOI - 10.2298/pim1103019o

Subject(s) - convolution (computer science) , mathematics , product (mathematics) , univariate , distribution (mathematics) , combinatorics , function (biology) , distribution function , multivariate statistics , mathematical analysis , pure mathematics , statistics , physics , geometry , thermodynamics , computer science , machine learning , evolutionary biology , artificial neural network , biology

Assume that X→ and Y→ are independent, nonnegative d-dimensional random vectors with distribution function (d.f.) F(x→) and G(x→), respectively. We are interested in estimates for the difference between the product and the convolution product of F and G, i.e., D(x→) = F(x→)G(x→) − F ∗ G(x→). Related to D(x→) is the difference R(x→) between the tail of the convolution and the sum of the tails: R(x→) = (1 − F ∗ G(x→))−(1 − F(x→) + 1 − G(x→)). We obtain asymptotic inequalities and asymptotic equalities for D(x→) and R(x→). The results are multivariate analogues of univariate results obtained by several authors before.

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