Bivariate stopped-sum distributions using saddlepoint methods

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.