On Characterizations of a Mixture of Exponential Distributions

Several results characterizing a mixture of exponential distributions are presented. Section 2 generalizes two of Govindarajulu´s results, using sequences of moments of order statistics. A necessary and sufficient condition is given in section 3 that an absolutely continuous positive r.v. follow a mixture of two exponential distributions. The conditions are based on the absolute difference of two i.i.d. random variables. Using conditional s-expectations, we generalize Shanbhag´s result, in section 4.