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On some properties of the mean inactivity time function

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  • Khan, Ruhul Ali
  • Bhattacharyya, Dhrubasish
  • Mitra, Murari

Abstract

Different aspects of mean inactivity time (MIT) function such as properties, bounds and limiting behaviour are studied. We proceed to prove an important characterization theorem and also explore weak convergence issues. Finally, connections between MIT and reversed hazard rate functions are examined.

Suggested Citation

  • Khan, Ruhul Ali & Bhattacharyya, Dhrubasish & Mitra, Murari, 2021. "On some properties of the mean inactivity time function," Statistics & Probability Letters, Elsevier, vol. 170(C).
    • Handle: RePEc:eee:stapro:v:170:y:2021:i:c:s0167715220302960
    DOI: 10.1016/j.spl.2020.108993
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    References listed on IDEAS

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    1. Masaaki Kijima & Masamitsu Ohnishi, 1999. "Stochastic orders and their applications in financial optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(2), pages 351-372, October.
    2. Eeckhoudt, Louis & Gollier, Christian, 1995. "Demand for Risky Assets and the Monotone Probability Ratio Order," Journal of Risk and Uncertainty, Springer, vol. 11(2), pages 113-122, September.
    3. J. Ruiz & J. Navarro, 1996. "Characterizations based on conditional expectations of the doubled truncated distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(3), pages 563-572, September.
    4. Arijit Patra & Chanchal Kundu, 2020. "Further results on residual life and inactivity time at random time," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(5), pages 1261-1271, March.
    5. Sengupta, Debasis & Das, Sudipta, 2016. "Sharp bounds on DMRL and IMRL classes of life distributions with specified mean," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 101-107.
    6. S. Goliforushani & M. Asadi, 2008. "On the discrete mean past lifetime," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(2), pages 209-217, September.
    7. Bhattacharyya, Dhrubasish & Khan, Ruhul Ali & Mitra, Murari, 2020. "A nonparametric test for comparison of mean past lives," Statistics & Probability Letters, Elsevier, vol. 161(C).
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    Cited by:

    1. Khan, Ruhul Ali, 2023. "Two-sample nonparametric test for proportional reversed hazards," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    2. Mathew, Litty & P., Anisha & Kattumannil, Sudheesh K., 2022. "A jackknife empirical likelihood ratio test for strong mean inactivity time order," Statistics & Probability Letters, Elsevier, vol. 190(C).

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