The difference between the product and the convolution product of distribution functions in R-n

E. Omey*, R. Vesilo

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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., Related to D(x) is the difference R(x) between the tail of the convolution and the sum of the tails. 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.

Original languageEnglish
Pages (from-to)19-36
Number of pages18
JournalPublications de l'Institut Mathematique
Volume89
Issue number103
DOIs
Publication statusPublished - 2011

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