Sum of Independent XGamma Distributions

The XGamma distribution is a generated distribution from a mixture of Exponential and Gamma distributions. It is found that in many cases the XGamma has more flexibility than the Exponential distribution. In this paper we consider the sum of independent XGamma distributions with different parameters. We showed that the probability density function of this distribution is a sum of the probability density function of the Erlang distributions. As a consequence, we find exact closed expressions of the other related statistical functions. Next, we examine the estimation of the parameters by maximum likelihood estimators. We observe in an applications a real data set which shows that this model provides better fit to the data as compared to the sum of the Exponential distributions, the Hypoexponential models.