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

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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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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Keywords

  • Common shock model
  • Generalized Pólya process
  • Multivariate new better than used (MNBU) distribution
  • Stochastic dependence
  • Ageing property

Mathematics Subject Classification

  • 60E05
  • 60E15
  • 62H86