Abstract
Eventhough considerable research is now available on the study of entropy using quantile function, a bivariate extension of the same has not been considered so far. In the present study, we propose a quantile version of a vector-valued bivariate differential entropy function in the past life and study its various properties. We prove characterization theorems for some well-known quantile lifetime models. It is shown that the proposed measure uniquely determines the quantile function. We also study various reliability properties of quantile-based bivariate past entropy and examine its usefulness through a real data set.
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Acknowledgements
The authors are grateful to the editor and referees for their constructive comments. The first author wishes to thank Cochin University of Science and Technology, India, for the financial support. The third and fourth authors wish to thank the Science and Engineering Research Board (SERB), Government of India (FILE NO.MTR/2020/000051 vide Diary No.SERB/F/5424/2020-2021 dated 10-12-2020 and FILE NO.MTR/2019/000203 vide Diary No.SERB/F/9880/2019-2020 dated 06-02-2020) for the financial support.
Funding
This work was supported by grants from the Cochin University of Science and Technology, India and Science and Engineering Research Board (SERB), Government of India (FILE NO.MTR/2020/000051 vide Diary No.SERB/F/5424/2020-2021 dated 10-12-2020 and FILE NO.MTR/2019/000203 vide Diary No.SERB/F/9880/2019-2020 dated 06-02-2020).
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Subhash, S., Nair, N.U., Sunoj, S.M. et al. Bivariate Quantile-Based Entropy in Past Lifetime. J Indian Soc Probab Stat 23, 187–209 (2022). https://doi.org/10.1007/s41096-022-00120-x
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DOI: https://doi.org/10.1007/s41096-022-00120-x