Bounds for Some General Sums of Random Variables

Statistics & Probability Letters, Vol. 81, No. 3, pp. 382-391, March 2011

16 Pages Posted: 12 Jun 2011  

Steven Vanduffel

Vrije Universiteit Brussel (VUB)

Zinoviy Landsman

University of Haifa, Department of Statistics

Date Written: November 1, 2010

Abstract

Rogers & Shi (1995) have used the technique of conditional expectations to derive approximations for the distribution of a sum of lognormals. In this paper we extend their results to more general sums of random variables. In particular we study sums of functions of dependent random variables that are multivariate normally distributed and also derive results for sums of functions of dependent random variables from the additive exponential dispersion family. The usefulness of our results for practical applications is also discussed.

Keywords: Bounds, Dependence, Exponential Dispersion Family

Suggested Citation

Vanduffel, Steven and Landsman, Zinoviy, Bounds for Some General Sums of Random Variables (November 1, 2010). Statistics & Probability Letters, Vol. 81, No. 3, pp. 382-391, March 2011. Available at SSRN: https://ssrn.com/abstract=1862863

Steven Vanduffel (Contact Author)

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
Brussels, Brabant 1050
Belgium

HOME PAGE: http://www.stevenvanduffel.com

Zinoviy Landsman

University of Haifa, Department of Statistics ( email )

Haifa, 31905
Israel
+972-4-8249003 (Phone)

HOME PAGE: http://stat.haifa.ac.il/~landsman

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