The n-fold convolution of generalized exponential-sum distribution functions

摘要

For continuous random variables, their distribution data can be approximated to generalized exponential-sum distribution functions by optimization tools like TOMLAB. Generalized exponential-sum distribution functions have larger representations and wider applications than pure exponential-sum distribution functions. On the bases of the n-fold convolution of pure exponential-sum distribution functions, the n-fold convolution of generalized exponential-sum distribution functions has been developed in this paper. Compared with the n-fold convolution of pure exponential-sum distribution functions, the results presented in this paper for the calculation of the n-fold convolution of generalized exponential-sum distribution functions are more general and applicable. As a matter of fact, the solution for computing the n-fold convolution of pure exponential-sum distribution functions is contained in the solution for the calculation of the n-fold convolution of generalized exponential-sum distribution functions. Limited testing results show that the formulae presented in this paper are correct.