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Bivariate stopped-sum distributions using saddlepoint methods. (English) Zbl 1310.60017

Summary: This paper introduces the bivariate saddlepoint approximations of the cumulative distribution function to bivariate stopped-sum distributions class in continuous and discrete settings. We discuss approximations to bivariate stopped-sum random vectors with dependent components assuming existence of the joint moment generating function. Special attention is given to Poisson stopped-sum family. Numerical examples of continuous and discrete distributions from the Poisson stopped-sum family are presented.

MSC:

60E99 Distribution theory
60G50 Sums of independent random variables; random walks
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