On a Parametric Estimation for a Convolution of Exponential Densities

Abstract

Broad application of the continuous-time Markov chain is caused by memoryless property of exponential distribution. An employment of non-exponential distributions leads to remarkable analytical difficulties. The usage of arbitrary non-negative density approximation by a convolution of exponential densities is a way of considerable interest. Two aspects of the problem solution are considered. First, the parametrical estimation of the convolution on the basis of given statistical data. Second, an approximation of fixed non-negative density. An approximation and estimation are performed by the method of the moments, maximum likelihood method, and fitting of a density. An empirical analysis of different approaches has been performed with the use of simulation. The efficiency of the considered approach is illustrated by the task of the queuing theory.