具有 Max-U-Exp 混合变量的混合泊松过程——工作版本
Mixed Poisson process with Max-U-Exp mixing variable -- Working version
AI总结：
本文定义并研究了 Max-U-Exp 分布及其参数的矩估计方法，基于混合泊松过程理论构建了具有 Max-U-Exp 混合变量的混合泊松过程，并推导了其相关分布与数字特征。
摘要：
本工作定义并研究了 Max-U-Exp 分布的性质。应用矩方法来估计其参数。然后，利用 Grandel（1997）以及 Karlis 和 Xekalaki（2005）发展的关于混合泊松过程的一般理论，类比 Jordanova 等人（2023）以及 Jordanova 和 Stehlik（2017）的工作，定义并研究了与该混合泊松过程特例相关的新随机向量和随机变量的性质。Exp-Max-U-Exp 分布得到了定义和深入研究。它作为具有 Max-U-Exp 混合变量的混合泊松过程中到达间隔时间的分布自然出现。更新时刻的分布被称为 Erlang-Max-U-Exp，并通过其概率密度函数进行定义。随后研究了其性质。最后，定义了相应的具有 Max-U-Exp 混合变量的混合泊松过程。求出了其有限维分布和条件分布，并确定了它们的数字特征。
英文摘要：
This work defines and investigates the properties of the Max-U-Exp distribution. The method of moments is applied in order to estimate its parameters. Then, by using the previous general theory about Mixed Poisson processes, developed by Grandel (1997), and Karlis and Xekalaki (2005), and analogously to Jordanova et al. (2023), and Jordanova and Stehlik (2017) we define and investigate the properties of the new random vectors and random variables, which are related with this particular case of a Mixed Poisson process. Exp-Max-U-Exp distribution is defined and thoroughly investigated. It arises in a natural way as a distribution of the inter-arrival times in the Mixed Poisson process with Max-U-Exp mixing variable. The distribution of the renewal moments is called Erlang-Max-U-Exp and is defined via its probability density function. Investigation of its properties follows. Finally, the corresponding Mixed Poisson process with Max-U-Exp mixing variable is defined. Its finite dimensional and conditional distributions are found and their numerical characteristics are determined.
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