Mixed Poisson process with Stacy mixing variable

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Stochastic Analysis and Applications Pub Date : 2023-03-17 DOI:10.1080/07362994.2023.2242471

P. Jordanova, Mladen Savov, Assen Tchorbadjieff, Milan Stehl'ik

{"title":"Mixed Poisson process with Stacy mixing variable","authors":"P. Jordanova, Mladen Savov, Assen Tchorbadjieff, Milan Stehl'ik","doi":"10.1080/07362994.2023.2242471","DOIUrl":null,"url":null,"abstract":"Stacy distribution defined for the first time in 1961 provides a flexible framework for modelling of a wide range of real-life behaviours. It appears under different names in the scientific literature and contains many useful particular cases. Homogeneous Poisson processes are appropriate apriori models for the number of renewals up to a given time $t>0$. This paper mixes them and considers a Mixed Poisson process with Stacy mixing variable. We call it a Poisson-Stacy process. The resulting counting process is one of the Generalised Negative Binomial processes, and the distribution of its time-intersections are very-well investigated in the scientific literature. Here we define and investigate their joint probability distributions. Then, the corresponding mixed renewal process is investigated and Exp-Stacy and Erlang-Stacy distributions are defined and partially studied. The paper finishes with a simulation study of these stochastic processes. Some plots of the probability density functions, probability mass functions, mean square regressions and sample paths are drawn together with the corresponding code for the simulations.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2023-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Stochastic Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/07362994.2023.2242471","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

Abstract

Stacy distribution defined for the first time in 1961 provides a flexible framework for modelling of a wide range of real-life behaviours. It appears under different names in the scientific literature and contains many useful particular cases. Homogeneous Poisson processes are appropriate apriori models for the number of renewals up to a given time $t>0$. This paper mixes them and considers a Mixed Poisson process with Stacy mixing variable. We call it a Poisson-Stacy process. The resulting counting process is one of the Generalised Negative Binomial processes, and the distribution of its time-intersections are very-well investigated in the scientific literature. Here we define and investigate their joint probability distributions. Then, the corresponding mixed renewal process is investigated and Exp-Stacy and Erlang-Stacy distributions are defined and partially studied. The paper finishes with a simulation study of these stochastic processes. Some plots of the probability density functions, probability mass functions, mean square regressions and sample paths are drawn together with the corresponding code for the simulations.

查看原文本刊更多论文

具有Stacy混合变量的混合泊松过程

1961年首次定义的史黛西分布为广泛的现实生活行为建模提供了一个灵活的框架。它在科学文献中以不同的名称出现，并包含许多有用的特殊案例。齐次泊松过程是适用于给定时间内更新次数的先验模型。本文将它们混合在一起，考虑了一个具有Stacy混合变量的混合泊松过程。我们称之为泊松-史黛西过程。由此产生的计数过程是广义负二项过程之一，其时间交叉点的分布在科学文献中得到了很好的研究。这里我们定义并研究它们的联合概率分布。然后，研究了相应的混合更新过程，定义了Exp-Stacy和Erlang-Stacy分布，并对其进行了部分研究。本文最后对这些随机过程进行了模拟研究。绘制了概率密度函数图、概率质量函数图、均方回归图和样本路径图，并给出了相应的仿真代码。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Stochastic Analysis and Applications 数学-统计学与概率论

CiteScore

2.70

自引率

7.70%

发文量

审稿时长

6-12 weeks

期刊介绍： Stochastic Analysis and Applications presents the latest innovations in the field of stochastic theory and its practical applications, as well as the full range of related approaches to analyzing systems under random excitation. In addition, it is the only publication that offers the broad, detailed coverage necessary for the interfield and intrafield fertilization of new concepts and ideas, providing the scientific community with a unique and highly useful service.