A new class of marginally regular multivariate counting processes generated by the mixture of multivariate Poisson processes

Ji Hwan Cha; F. G. Badía

doi:10.1080/03610926.2020.1812652

A new class of marginally regular multivariate counting processes generated by the mixture of multivariate Poisson processes

Ji Hwan Cha, F. G. Badía

Department of Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, a new class of marginally regular multivariate counting processes is developed and its stochastic properties are studied. The dependence of the proposed multivariate counting process is generated from two sources: by means of mixing and by sharing a common counting process. Even under a rather complex dependence structure, the stochastic properties of the multivariate process and its marginal processes are mathematically tractable. Initially, we define this multivariate counting process by means of mixing. For further characterization of it, we suggest an alternative definition, which facilitates convenient characterization of the proposed process. We derive the properties of the proposed multivariate counting process and analyze the multivariate dependence structure of the class.

Original language	English
Pages (from-to)	4235-4251
Number of pages	17
Journal	Communications in Statistics - Theory and Methods
Volume	51
Issue number	13
DOIs	https://doi.org/10.1080/03610926.2020.1812652
State	Published - 2022

Bibliographical note

Funding Information:
The work of the first author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant Number: 2019R1A6A1A11051177). The authors greatly thank the Associate Editor and the referee for helpful comments and advices, which have improved the presentation of this paper. The work of the second author has been supported by the Spanish government research projects MTM2015-63978 (MINECO-FEDER) and PGC2018-094964- B-100 (MINECO-FEDER).

Funding Information:
The authors greatly thank the Associate Editor and the referee for helpful comments and advices, which have improved the presentation of this paper. The work of the second author has been supported by the Spanish government research projects MTM2015-63978 (MINECO-FEDER) and PGC2018-094964- B-100 (MINECO-FEDER).

Publisher Copyright:
© 2020 Taylor & Francis Group, LLC.

Keywords

Generalized Polya process
complete intensity functions
dependence structure
marginally regular multivariate counting process

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10.1080/03610926.2020.1812652

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abstract = "In this paper, a new class of marginally regular multivariate counting processes is developed and its stochastic properties are studied. The dependence of the proposed multivariate counting process is generated from two sources: by means of mixing and by sharing a common counting process. Even under a rather complex dependence structure, the stochastic properties of the multivariate process and its marginal processes are mathematically tractable. Initially, we define this multivariate counting process by means of mixing. For further characterization of it, we suggest an alternative definition, which facilitates convenient characterization of the proposed process. We derive the properties of the proposed multivariate counting process and analyze the multivariate dependence structure of the class.",

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AB - In this paper, a new class of marginally regular multivariate counting processes is developed and its stochastic properties are studied. The dependence of the proposed multivariate counting process is generated from two sources: by means of mixing and by sharing a common counting process. Even under a rather complex dependence structure, the stochastic properties of the multivariate process and its marginal processes are mathematically tractable. Initially, we define this multivariate counting process by means of mixing. For further characterization of it, we suggest an alternative definition, which facilitates convenient characterization of the proposed process. We derive the properties of the proposed multivariate counting process and analyze the multivariate dependence structure of the class.

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ER -

A new class of marginally regular multivariate counting processes generated by the mixture of multivariate Poisson processes

Abstract

Bibliographical note

Keywords

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