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On past geometric vitality function of order statistics

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Abstract

In this article, we propose geometric vitality function introduced by Nair and Rajesh (IAPQR Trans 25(1):1–8, 2000) for the past lifetime of a random variable. This measure plays a vital role in analysing different characteristics of a system/component when it fails in the interval (0, t). The monotonic behaviour and some ordering properties in terms of the proposed measure were studied under certain conditions. Similar properties of the proposed measure were analysed for order statistics as well. Further, bounds were obtained for the past geometric vitality function of order statistics. Apart from this, characterizations of some lifetime probability distributions with respect to order statistics were also discussed.

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Acknowledgements

We are thankful to the Editor in Chief for his/her constructive suggestions and the anonymous referee for his remarks, both which substantially improved the paper. The second author wishes to thank Science Engineering Research Board, Govt. of India for supporting this research in the form of MATRICS project.

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Authors and Affiliations

  1. Department of Statistics, University of Kerala, Kariavattom, Trivandrum, 695581, India

    Ramanathan Gayathri & Enchakudiyil Ibrahim Abdul Sathar

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  1. Ramanathan Gayathri
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  2. Enchakudiyil Ibrahim Abdul Sathar
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Correspondence to Enchakudiyil Ibrahim Abdul Sathar.

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Gayathri, R., Abdul Sathar, E.I. On past geometric vitality function of order statistics. Metrika 84, 263–280 (2021). https://doi.org/10.1007/s00184-020-00789-9

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  • DOI: https://doi.org/10.1007/s00184-020-00789-9

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