The Use of Fractional Moments for Estimating the Parameters of a Mixed Exponential Distribution

In this paper the use of fractional moments for estimation purposes is discussed. These ideas are illustrated by means of the mixed exponential distribution. The estimation of the three parameters of the above distribution by the method of moments and by maximum likelihood is investigated numerically in detail. As anticipated, the efficiency of the former method can be greatly increased by using approximately optimal combinations of moments. It is found that the moment method requires only a small amount of calculation when compared with the maximum likelihood method, although charts are presented to greatly ease the computational burden of the latter method.