SADDLEPOINT APPROXIMATION TO THE CUMULATIVE DISTRIBUTION FUNCTION FOR A LINEAR COMBINATION OF CONVOLUTION GAMMA–EXPONENTIAL MODELS Page No: 3259-3265

Mutairi Alya and Heng Chin Low

Keywords: Gamma-Exponential distribution, Saddlepoint approximation, moment generating function, linear combinations of convolutions.

Abstract: This paper derives the saddlepoint approximation for a linear combination of the convolution ? , where and ? are real constants and ? and ? denote Gamma and Exponential random variables, respectively, and are distributed independently of each other. We also discuss the generalization of this convolution (i.e., the convolution of the convolution for Gamma-Exponential random variables), which is unknown and extremely difficult to obtain. The associated saddlepoint approximation CDFs are derived, and plots of the CDFs and some measures of the center and spread of the new approximations are given.



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