论文标题
关于一类随机总和的分布及其应用
On Distributions of One Class of Random Sums and their Applications
论文作者
论文摘要
我们提出了研究随机变量随机总和的性质的结果。我们考虑案例，其中汇总数是事件发生的第一刻。提出了一个积分方程，以确定随机总和的分布。在获得的结果的帮助下，我们分析了Geiger-Muller Counter不会丢失任何粒子的时间的分布功能，具有更新的冗余系统的繁忙周期的分布函数以及单人类排队系统的寄居时间的分布函数。
We propose results of the investigation of properties of the random sums of random variables. We consider the case, where the number of summands is the first moment of an event occurrence. An integral equation is presented that determines distributions of random sums. With the help of the obtained results we analyse the distribution function of the time during which the Geiger-Muller counter will not lose any particles, the distribution function of the busy period of a redundant system with renewal, and the distribution function of the sojourn times of a single-server queueing system.
