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On past geometric vitality function of order statistics

Author

Listed:
  • Ramanathan Gayathri

    (University of Kerala)

  • Enchakudiyil Ibrahim Abdul Sathar

    (University of Kerala)

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.

Suggested Citation

  • Ramanathan Gayathri & Enchakudiyil Ibrahim Abdul Sathar, 2021. "On past geometric vitality function of order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(2), pages 263-280, February.
    • Handle: RePEc:spr:metrik:v:84:y:2021:i:2:d:10.1007_s00184-020-00789-9
    DOI: 10.1007/s00184-020-00789-9
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    References listed on IDEAS

    as
    1. Vikas Kumar & H. Taneja & R. Srivastava, 2011. "A dynamic measure of inaccuracy between two past lifetime distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(1), pages 1-10, July.
    2. Di Crescenzo, Antonio & Longobardi, Maria, 2004. "A measure of discrimination between past lifetime distributions," Statistics & Probability Letters, Elsevier, vol. 67(2), pages 173-182, April.
    3. Goel, Ritu & Taneja, H.C. & Kumar, Vikas, 2018. "Measure of entropy for past lifetime and k-record statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 623-631.
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