On past geometric vitality function of order statistics

Ramanathan Gayathri () and Enchakudiyil Ibrahim Abdul Sathar ()
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Ramanathan Gayathri: University of Kerala
Enchakudiyil Ibrahim Abdul Sathar: University of Kerala

Metrika: International Journal for Theoretical and Applied Statistics, 2021, vol. 84, issue 2, No 7, 263-280

Abstract: 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.

Keywords: Past geometric vitality function; Order statistics; Monotone property; Characterizations; 62B10; 94A17 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00184-020-00789-9

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