Explicit Bounds for the Distribution Function of the Sum of Dependent Normally Distributed Random Variables

Mathematics – Probability

Scientific paper

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Keywords: Dependent RVs, Copulas, Frechet Bounds

Scientific paper

In this paper an analytic expression is given for the bounds of the
distribution function of the sum of dependent normally distributed random
variables. Using the theory of copulas and the important Frechet bounds the
dependence structure is not restricted to any specific type. Numerical
illustrations are provided to assess the quality of the derived bounds.

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