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Weighted Mean Inactivity Time Function with Applications

Author

Listed:
  • Antonio Di Crescenzo

    (Dipartimento di Matematica, Università degli Studi di Salerno, Via Giovanni Paolo II n. 132, I-84084 Fisciano, SA, Italy
    These authors contributed equally to this work.)

  • Abdolsaeed Toomaj

    (Department of Mathematics and Statistics, Faculty of Basic Sciences and Engineering, Gonbad Kavous University, Gonbad 4971799151, Iran
    These authors contributed equally to this work.)

Abstract

We consider an extension of the mean inactivity time based on a non-negative weight function. We show various properties of the new notion, and relate it to various functions of interest in reliability theory and information measures, such as the dynamic cumulative entropy, the past entropy, the varentropy, and the weighted cumulative entropy. Moreover, based on the comparison of weighted mean inactivity times, we introduce and study a new stochastic order and compare it with other suitable orders. We also discuss some results about the variance of transformed random variables and the weighted generalized cumulative entropy. Then, we investigate certain connections with the location-independent riskier order. Finally, we pinpoint several characterizations and preservation properties of the new stochastic order under shock models, random maxima, and notions of renewal theory.

Suggested Citation

  • Antonio Di Crescenzo & Abdolsaeed Toomaj, 2022. "Weighted Mean Inactivity Time Function with Applications," Mathematics, MDPI, vol. 10(16), pages 1-30, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2828-:d:883755
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    References listed on IDEAS

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