Stochastic comparisons and multivariate dependence for the epoch times of trend renewal processes

Francisco German Badía; Carmen Sangüesa; Ji Hwan Cha

doi:10.1016/j.jmva.2018.07.011

Stochastic comparisons and multivariate dependence for the epoch times of trend renewal processes

Francisco German Badía, Carmen Sangüesa, Ji Hwan Cha

Department of Statistics

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

3 Scopus citations

Abstract

In this paper we study stochastic comparisons and dependence properties for the epoch and inter-epoch times of trend renewal processes with different trend functions. These results extend some of the results on the non-homogeneous Poisson process in Belzunce et al. (2001, 2003) to trend renewal processes. Some applications of the results to a shock model, a repair process, and a specific class of intermediate order statistics are provided.

Original language	English
Pages (from-to)	174-184
Number of pages	11
Journal	Journal of Multivariate Analysis
Volume	168
DOIs	https://doi.org/10.1016/j.jmva.2018.07.011
State	Published - Nov 2018

Bibliographical note

Funding Information:
The authors greatly appreciate the Editor’s and referees’ helpful comments and advice. The work of the first two authors was supported by the Spanish government under research project MTM2015-63978 (MINECO/FEDER). The work of Ji Hwan Cha was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2016R1A2B2014211 ). The work of Ji Hwan Cha was also supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2009-0093827 ).

Publisher Copyright:
© 2018 Elsevier Inc.

Keywords

Multivariate dependence
Multivariate stochastic orders
Trend renewal
order statistics

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10.1016/j.jmva.2018.07.011

Cite this

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title = "Stochastic comparisons and multivariate dependence for the epoch times of trend renewal processes",

abstract = "In this paper we study stochastic comparisons and dependence properties for the epoch and inter-epoch times of trend renewal processes with different trend functions. These results extend some of the results on the non-homogeneous Poisson process in Belzunce et al. (2001, 2003) to trend renewal processes. Some applications of the results to a shock model, a repair process, and a specific class of intermediate order statistics are provided.",

keywords = "Multivariate dependence, Multivariate stochastic orders, Trend renewal, order statistics",

author = "Bad{\'i}a, {Francisco German} and Carmen Sang{\"u}esa and Cha, {Ji Hwan}",

note = "Funding Information: The authors greatly appreciate the Editor{\textquoteright}s and referees{\textquoteright} helpful comments and advice. The work of the first two authors was supported by the Spanish government under research project MTM2015-63978 (MINECO/FEDER). The work of Ji Hwan Cha was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2016R1A2B2014211 ). The work of Ji Hwan Cha was also supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2009-0093827 ). Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

year = "2018",

month = nov,

doi = "10.1016/j.jmva.2018.07.011",

language = "English",

volume = "168",

pages = "174--184",

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T1 - Stochastic comparisons and multivariate dependence for the epoch times of trend renewal processes

AU - Badía, Francisco German

AU - Sangüesa, Carmen

AU - Cha, Ji Hwan

N1 - Funding Information: The authors greatly appreciate the Editor’s and referees’ helpful comments and advice. The work of the first two authors was supported by the Spanish government under research project MTM2015-63978 (MINECO/FEDER). The work of Ji Hwan Cha was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2016R1A2B2014211 ). The work of Ji Hwan Cha was also supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2009-0093827 ). Publisher Copyright: © 2018 Elsevier Inc.

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N2 - In this paper we study stochastic comparisons and dependence properties for the epoch and inter-epoch times of trend renewal processes with different trend functions. These results extend some of the results on the non-homogeneous Poisson process in Belzunce et al. (2001, 2003) to trend renewal processes. Some applications of the results to a shock model, a repair process, and a specific class of intermediate order statistics are provided.

AB - In this paper we study stochastic comparisons and dependence properties for the epoch and inter-epoch times of trend renewal processes with different trend functions. These results extend some of the results on the non-homogeneous Poisson process in Belzunce et al. (2001, 2003) to trend renewal processes. Some applications of the results to a shock model, a repair process, and a specific class of intermediate order statistics are provided.

KW - Multivariate dependence

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KW - order statistics

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SP - 174

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JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

ER -

Stochastic comparisons and multivariate dependence for the epoch times of trend renewal processes

Abstract

Bibliographical note

Keywords

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