Tóm tắt:

In this paper, we investigate the mixture of Erlang and exponential approximation based on the first three moments and the matrix-exponential representation of mixed Erlang and exponential functions. Besides, a number of numerical examples are given to illustrate the quick convergence of the method in the cases of the first three moments of uniform distribution on . Moreover to illustrate this method, a numerical example is given with different initial reserves of insurance company.