Although Poisson processes are widely used in various applications for modeling of recurrent point events, there exist obvious limitations. Several specific mixed Poisson processes (which are formally not Poisson processes any more) that were recently introduced in the literature overcome some of these limitations. In this paper, we define a general mixed Poisson process with the phase-type (PH) distribution as the mixing one. As the PH distribution is dense in the set of lifetime distributions, the new process can be used to approximate any mixed Poisson process. We study some basic stochastic properties of the new process and discuss relevant applications by considering the extreme shock model, the stochastic failure rate model and the \(\delta\)-shock model.

尽管泊松过程被广泛用于对循环点事件进行建模的各种应用中，但存在明显的局限性。最近在文献中引入的几个特定的​​混合泊松过程（正式不再是泊松过程）克服了其中的一些限制。在本文中，我们定义了一个以相型（PH）分布为混合的一般混合泊松过程。由于 PH 分布在一组寿命分布中是密集的，因此新过程可用于逼近任何混合 Poisson 过程。我们研究了新过程的一些基本随机特性，并通过考虑极端冲击模型、随机失效率模型和\(\delta\) -shock 模型讨论了相关应用。