IDEAS home Printed from https://ideas.repec.org/a/spr/sankha/v84y2022i2d10.1007_s13171-020-00222-3.html
   My bibliography  Save this article

Stochastic Comparisons of General Proportional Mean Past Lifetime Frailty Model

Author

Listed:
  • Fatemeh Hooti

    (Ferdowsi University of Mashhad)

  • Jafar Ahmadi

    (Ferdowsi University of Mashhad)

  • N. Balakrishnan

    (McMaster University)

Abstract

In this paper, the general proportional mean past lifetime frailty model is considered, from which the unconditional cumulative distribution and density functions of the lifetime variable are derived. Dependency between the two variables are studied. Stochastic comparisons are made through which it is shown that some well-known stochastic orderings between two frailty variables carry over to the corresponding lifetime variables. The effects of baseline variable and the frailty variable on the proposed frailty model are studied. The relative mean past lifetime ordering is introduced and some relative ordering between two lifetime random variables with different frailty variables are studied. Also a simulation study is given to illustrate some results.

Suggested Citation

  • Fatemeh Hooti & Jafar Ahmadi & N. Balakrishnan, 2022. "Stochastic Comparisons of General Proportional Mean Past Lifetime Frailty Model," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 844-866, August.
    • Handle: RePEc:spr:sankha:v:84:y:2022:i:2:d:10.1007_s13171-020-00222-3
    DOI: 10.1007/s13171-020-00222-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13171-020-00222-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13171-020-00222-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. David D. Hanagal & Arvind Pandey, 2020. "Correlated inverse Gaussian frailty models for bivariate survival data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(4), pages 845-863, February.
    2. Majid Rezaei, 2016. "On proportional mean past lifetimes model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(14), pages 4035-4047, July.
    3. Khaledi, Baha-Eldin & Shaked, Moshe, 2010. "Stochastic comparisons of multivariate mixtures," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2486-2498, November.
    4. Majid Rezaei & Behzad Gholizadeh, 2015. "On the Mixture Proportional Mean Residual Life Model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(20), pages 4263-4277, October.
    5. Majid Rezaei & Behzad Gholizadeh & Salman Izadkhah, 2015. "On Relative Reversed Hazard Rate Order," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(2), pages 300-308, January.
    6. Kayid, M. & Izadkhah, S. & Abouammoh, A.M., 2019. "Proportional reversed hazard rates weighted frailty model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 528(C).
    7. James Vaupel & Kenneth Manton & Eric Stallard, 1979. "The impact of heterogeneity in individual frailty on the dynamics of mortality," Demography, Springer;Population Association of America (PAA), vol. 16(3), pages 439-454, August.
    8. Finkelstein, Maxim, 2006. "On relative ordering of mean residual lifetime functions," Statistics & Probability Letters, Elsevier, vol. 76(9), pages 939-944, May.
    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. M. Kayid & S. Izadkhah & Ming J. Zuo, 2017. "Some results on the relative ordering of two frailty models," Statistical Papers, Springer, vol. 58(2), pages 287-301, June.
    2. Neeraj Misra & Jisha Francis, 2020. "Relative ageing in frailty and resilience models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(2), pages 171-196, February.
    3. Misra, Neeraj & Francis, Jisha, 2015. "Relative ageing of (n−k+1)-out-of-n systems," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 272-280.
    4. F. G. Badía & Ji Hwan Cha, 2017. "On bending (down and up) property of reliability measures in mixtures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(4), pages 455-482, May.
    5. Elham Khaleghpanah Noughabi & Majid Chahkandi & Majid Rezaei, 2022. "On the Mean and Variance Residual Life Comparisons of Coherent Systems with Identically Distributed Components," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2801-2822, December.
    6. Neeraj Misra & Jisha Francis, 2018. "Relative aging of (n − k + 1)‐out‐of‐n systems based on cumulative hazard and cumulative reversed hazard functions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(6-7), pages 566-575, September.
    7. Bagdonavicius, Vilijandas & Nikulin, Mikhail, 2000. "On goodness-of-fit for the linear transformation and frailty models," Statistics & Probability Letters, Elsevier, vol. 47(2), pages 177-188, April.
    8. Yahia Salhi & Pierre-Emmanuel Thérond, 2016. "Age-Specific Adjustment of Graduated Mortality," Working Papers hal-01391285, HAL.
    9. Feehan, Dennis & Wrigley-Field, Elizabeth, 2020. "How do populations aggregate?," SocArXiv 2fkw3, Center for Open Science.
    10. M. K. Lintu & Asha Kamath, 2022. "Performance of recurrent event models on defect proneness data," Annals of Operations Research, Springer, vol. 315(2), pages 2209-2218, August.
    11. Il Do Ha & Maengseok Noh & Youngjo Lee, 2010. "Bias Reduction of Likelihood Estimators in Semiparametric Frailty Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 307-320, June.
    12. N. Unnikrishnan Nair & S. M. Sunoj & Rajesh G., 2023. "Relation between Relative Hazard Rates and Residual Divergence with some Applications to Reliability Analysis," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 784-802, February.
    13. Andreas Wienke & Anne M. Herskind & Kaare Christensen & Axel Skytthe & Anatoli I. Yashin, 2002. "The influence of smoking and BMI on heritability in susceptibility to coronary heart disease," MPIDR Working Papers WP-2002-003, Max Planck Institute for Demographic Research, Rostock, Germany.
    14. Filipe Costa Souza & Wilton Bernardino & Silvio C. Patricio, 2024. "How life-table right-censoring affected the Brazilian social security factor: an application of the gamma-Gompertz-Makeham model," Journal of Population Research, Springer, vol. 41(3), pages 1-38, September.
    15. Svetlana V. Ukraintseva & Anatoli I. Yashin, 2005. "Economic progress as cancer risk factor. I: Puzzling facts of cancer epidemiology," MPIDR Working Papers WP-2005-021, Max Planck Institute for Demographic Research, Rostock, Germany.
    16. Silke van Daalen & Hal Caswell, 2015. "Lifetime reproduction and the second demographic transition: Stochasticity and individual variation," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 33(20), pages 561-588.
    17. K. Motarjem & M. Mohammadzadeh & A. Abyar, 2020. "Geostatistical survival model with Gaussian random effect," Statistical Papers, Springer, vol. 61(1), pages 85-107, February.
    18. Schultz, T. Paul, 2010. "Population and Health Policies," Handbook of Development Economics, in: Dani Rodrik & Mark Rosenzweig (ed.), Handbook of Development Economics, edition 1, volume 5, chapter 0, pages 4785-4881, Elsevier.
    19. Xu, Linzhi & Zhang, Jiajia, 2010. "An EM-like algorithm for the semiparametric accelerated failure time gamma frailty model," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1467-1474, June.
    20. Carlos Díaz-Venegas, 2014. "Identifying the Confounders of Marginalization and Mortality in Mexico, 2003–2007," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 118(2), pages 851-875, September.

    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:spr:sankha:v:84:y:2022:i:2:d:10.1007_s13171-020-00222-3. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.