标题： 独立 XGamma 分布的和 显示英文标题

标题： Sum of Independent XGamma Distributions

摘要： XGamma 分布是从指数分布和伽马分布的混合分布生成的分布。结果表明，在许多情况下，XGamma 分布比指数分布具有更大的灵活性。本文考虑了具有不同参数的独立 XGamma 分布的和。我们证明了该分布的概率密度函数是爱尔朗分布概率密度函数的和。因此，我们找到了其他相关统计函数的确切闭式表达。接下来，我们研究了通过最大似然估计量来估计参数的问题。在应用中，我们观察到一个实际数据集，结果显示此模型相对于指数分布的和、超指数模型，能更好地拟合数据。 显示英文摘要

摘要： 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.