On the distribution of the sum of independent exponential-geometric random variables


In this article, we derive exact expressions for the probability density function and cumulative distribution function of the sum of independent and non-identical exponential-geometric random variables. Then we discuss the corresponding result for independent and identically distributed exponential-geometric random variables. A saddlepoint approximation is also utilized to approximate the derived distribution. Finally, numerical simulations are used to investigate the precision of the saddlepoint approximation.

DOI Code: 10.1285/i20705948v16n3p694

Keywords: Exponential-geometric distribution; Divided differences; Independent and non-identically distributed random variables; Saddlepoint approximation.


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