论文标题
指数和低指数分布：一些特征
Exponential and Hypoexponential Distributions: Some Characterizations
论文作者
论文摘要
（一般）低指数分布是独立指数随机变量总和的分布。当涉及的指数变量具有不同的速率参数时，我们会考虑特定情况。我们证明以下相反的结果是正确的。如果对于某些$ n \ ge 2 $，$ x_1，x_2，\，\ ldots，\，x_n $是随机变量$ x $的独立副本，带有未知分布$ f $和$ x_j $的特定线性组合，则$ x_j $ he he he he he he he he he hat and appepartients分发，那么$ f $是指数的。因此，我们获得了指数分布的新特征。作为主要结果的推论，我们扩展了Arnold和Villaseñor（2013）最近建立的一些以前的特征，以实现两个随机变量的特定卷积。
The (general) hypoexponential distribution is the distribution of a sum of independent exponential random variables. We consider the particular case when the involved exponential variables have distinct rate parameters. We prove that the following converse result is true. If for some $n\ge 2$, $X_1, X_2,\,\ldots,\,X_n$ are independent copies of a random variable $X$ with unknown distribution $F$ and a specific linear combination of $X_j$'s has hypoexponential distribution, then $F$ is exponential. Thus, we obtain new characterizations of the exponential distribution. As corollaries of the main results, we extend some previous characterizations established recently by Arnold and Villaseñor (2013) for a particular convolution of two random variables.
