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A general multivariate new better than used (MNBU) distribution and its properties

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Abstract

In this paper, we develop a general multivariate new better than used (MNBU) distribution based on a multivariate common shock model. Assuming that the external shock process follows the generalized Pólya process and a shock can destroy each component with some given probability, the multivariate survival distribution is obtained. The dependence structure of the multivariate distribution is analyzed. The properties on the dependence order and the multivariate ageing are also studied. Finally, as a special case, we consider the distribution of the minimum random variable and briefly discuss its properties.

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Acknowledgements

The authors thank the reviewers for helpful comments and valuable suggestions, which have improved the presentation of this paper considerably. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2019R1A2B5B02069500). This work was also supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant Number: 2019R1A6A1A11051177).

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Authors and Affiliations

  1. Department of Statistics, Hankuk University of Foreign Studies, Yongin, 17035, Republic of Korea

    Hyunju Lee

  2. Department of Statistics, Ewha Womans University, Seoul, 120-750, Republic of Korea

    Ji Hwan Cha

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  1. Hyunju Lee
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  2. Ji Hwan Cha
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Correspondence to Ji Hwan Cha.

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Lee, H., Cha, J.H. A general multivariate new better than used (MNBU) distribution and its properties. Metrika 84, 27–46 (2021). https://doi.org/10.1007/s00184-020-00773-3

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  • DOI: https://doi.org/10.1007/s00184-020-00773-3

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