IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i16p2828-d883755.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/16/2828/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/16/2828/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Wentao Hu & Cuixia Chen & Yufeng Shi & Ze Chen, 2022. "A Tail Measure With Variable Risk Tolerance: Application in Dynamic Portfolio Insurance Strategy," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 831-874, June.
    2. Ian Jewitt, 1989. "Choosing Between Risky Prospects: The Characterization of Comparative Statics Results, and Location Independent Risk," Management Science, INFORMS, vol. 35(1), pages 60-70, January.
    3. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    4. Unnikrishnan Nair N. & Vineshkumar B., 2021. "Relation Between Cumulative Residual Entropy and Excess Wealth Transform with Applications to Reliability and Risk," Stochastics and Quality Control, De Gruyter, vol. 36(1), pages 43-57, June.
    5. Gupta, Ramesh C. & Peng, Cheng, 2009. "Estimating reliability in proportional odds ratio models," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1495-1510, February.
    6. P. Sankaran & V. Gleeja, 2008. "Proportional reversed hazard and frailty models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(3), pages 333-342, November.
    7. Belzunce, Félix & Martínez-Riquelme, Carolina & Ruiz, José M., 2013. "On sufficient conditions for mean residual life and related orders," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 199-210.
    8. P. Sankaran & S. Sunoj, 2004. "Identification of models using failure rate and mean residual life of doubly truncated random variables," Statistical Papers, Springer, vol. 45(1), pages 97-109, January.
    9. M. Chahkandi & J. Ahmadi & S. Baratpour, 2014. "Some results for repairable systems with minimal repairs," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 30(2), pages 218-226, March.
    10. Jorge Navarro & Nuria Torrado & Yolanda del Águila, 2018. "Comparisons Between Largest Order Statistics from Multiple-outlier Models with Dependence," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 411-433, March.
    11. Jorge Navarro, 2022. "Prediction of record values by using quantile regression curves and distortion functions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(6), pages 675-706, August.
    12. 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.
    13. Khorashadizadeh, M. & Rezaei Roknabadi, A.H. & Mohtashami Borzadaran, G.R., 2013. "Doubly truncated (interval) cumulative residual and past entropy," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1464-1471.
    14. Abdolsaeed Toomaj & Antonio Di Crescenzo, 2020. "Connections between Weighted Generalized Cumulative Residual Entropy and Variance," Mathematics, MDPI, vol. 8(7), pages 1-27, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Michèle Cohen & Isaac Meilijson, 2011. "In search of characterization of the preference for safety under the Choquet model," Post-Print halshs-00594082, HAL.
    2. Chateauneuf, Alain & Cohen, Michele & Meilijson, Isaac, 2004. "Four notions of mean-preserving increase in risk, risk attitudes and applications to the rank-dependent expected utility model," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 547-571, August.
    3. Aouani, Zaier & Chateauneuf, Alain, 2008. "Exact capacities and star-shaped distorted probabilities," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 185-194, September.
    4. Rolf Aaberge, 2002. "Characterization and Measurement of Duration Dependence in Hazard Rate Models," Discussion Papers 319, Statistics Norway, Research Department.
    5. Mao, Tiantian & Hu, Taizhong, 2012. "Characterization of left-monotone risk aversion in the RDEU model," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 413-422.
    6. Navarro, Jorge & Fernández-Martínez, Pedro, 2021. "Redundancy in systems with heterogeneous dependent components," European Journal of Operational Research, Elsevier, vol. 290(2), pages 766-778.
    7. Alain Chateauneuf & Michèle Cohen & Mina Mostoufi & Jean-Christophe Vergnaud, 2015. "Optimality of deductible for Yaari's model: a reappraisal," Documents de travail du Centre d'Economie de la Sorbonne 15072, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    8. Ryan, Matthew J., 2006. "Risk aversion in RDEU," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 675-697, September.
    9. Alain Chateauneuf & Michéle Cohen & Isaac Meilijson, 2005. "More pessimism than greediness: a characterization of monotone risk aversion in the rank-dependent expected utility model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(3), pages 649-667, April.
    10. Jorge Navarro & Franco Pellerey & Miguel A. Sordo, 2020. "Weak Dependence Notions and Their Mutual Relationships," Mathematics, MDPI, vol. 9(1), pages 1-27, December.
    11. Alain Chateauneuf & Michèle Cohen, 2008. "Cardinal extensions of EU model based on the Choquet integral," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00348822, HAL.
    12. Michèle Cohen, 2008. "Risk Perception, Risk Attitude and Decision : a Rank-Dependent Approach," Post-Print halshs-00348810, HAL.
    13. Robert, Christian Y. & Therond, Pierre-E., 2014. "Distortion Risk Measures, Ambiguity Aversion And Optimal Effort," ASTIN Bulletin, Cambridge University Press, vol. 44(2), pages 277-302, May.
    14. Patrick Moyes, 2007. "An extended Gini approach to inequality measurement," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(3), pages 279-303, December.
    15. Ghossoub, Mario & He, Xue Dong, 2021. "Comparative risk aversion in RDEU with applications to optimal underwriting of securities issuance," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 6-22.
    16. Fabio Maccheroni & Pietro Muliere & Claudio Zoli, 2005. "Inverse stochastic orders and generalized Gini functionals," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 529-559.
    17. Michèle Cohen & Isaac Meilijson, 2014. "Preference for safety under the Choquet model: in search of a characterization," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(3), pages 619-642, April.
    18. repec:hal:wpaper:hal-00813199 is not listed on IDEAS
    19. Johannes G. Jaspersen & Richard Peter & Marc A. Ragin, 2023. "Probability weighting and insurance demand in a unified framework," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 48(1), pages 63-109, March.
    20. Han Bleichrodt, 2022. "The prevention puzzle," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 47(2), pages 277-297, September.
    21. Mich�le Cohen, 2015. "Risk Perception, Risk Attitude, and Decision: A Rank-Dependent Analysis," Mathematical Population Studies, Taylor & Francis Journals, vol. 22(1), pages 53-70, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2828-:d:883755. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.