IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v127y2014icp151-159.html
   My bibliography  Save this article

On construction of general classes of bivariate distributions

Author

Listed:
  • Lee, Hyunju
  • Cha, Ji Hwan

Abstract

In this study, taking into account the physics of failure (death) and the interrelationship between the items involved, we propose a general methodology for constructing new ‘classes of bivariate distributions’. The approach is based on the stochastic modeling of the residual lifetime of an item after the failure of the other item. We derive the joint and the corresponding marginal distributions in a class constructed from the modeling of conditional failure rate. It is shown that the proposed new class includes several well-known bivariate distributions as special bivariate models. As illustrated, a number of new families of bivariate distributions are generated from the new class proposed in this paper. Furthermore, we briefly discuss the relationship to Freund’s bivariate exponential distribution.

Suggested Citation

  • Lee, Hyunju & Cha, Ji Hwan, 2014. "On construction of general classes of bivariate distributions," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 151-159.
    • Handle: RePEc:eee:jmvana:v:127:y:2014:i:c:p:151-159
    DOI: 10.1016/j.jmva.2014.02.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X1400030X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2014.02.007?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. Paul H. Kvam & Edsel A. Pena, 2005. "Estimating Load-Sharing Properties in a Dynamic Reliability System," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 262-272, March.
    2. Ji Hwan Cha & Jie Mi, 2011. "On a Stochastic Survival Model for a System Under Randomly Variable Environment," Methodology and Computing in Applied Probability, Springer, vol. 13(3), pages 549-561, September.
    3. Lee, Larry, 1979. "Multivariate distributions having Weibull properties," Journal of Multivariate Analysis, Elsevier, vol. 9(2), pages 267-277, June.
    4. Sarhan, Ammar M. & Balakrishnan, N., 2007. "A new class of bivariate distributions and its mixture," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1508-1527, August.
    5. Maxim Finkelstein & Ji Hwan Cha, 2013. "Burn-in for Heterogeneous Populations," Springer Series in Reliability Engineering, in: Stochastic Modeling for Reliability, edition 127, chapter 0, pages 261-312, Springer.
    6. Maxim Finkelstein & Ji Hwan Cha, 2013. "Shocks as Burn-in," Springer Series in Reliability Engineering, in: Stochastic Modeling for Reliability, edition 127, chapter 0, pages 313-361, Springer.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lee, Hyunju & Cha, Ji Hwan, 2015. "Construction of two new general classes of bivariate distributions based on stochastic orders," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 75-85.
    2. Hyunju Lee & Ji Hwan Cha, 2020. "A new general class of discrete bivariate distributions constructed by using the likelihood ratio," Statistical Papers, Springer, vol. 61(3), pages 923-944, June.
    3. Debasis Kundu, 2020. "On a General Class of Discrete Bivariate Distributions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 270-304, November.

    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. Alberti, Alexandre R. & Cavalcante, Cristiano A.V., 2020. "A two-scale maintenance policy for protection systems subject to shocks when meeting demands," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    2. Hazra, Nil Kamal & Finkelstein, Maxim & Cha, Ji Hwan, 2022. "On a hazard (failure) rate process with delays after shocks," Statistics & Probability Letters, Elsevier, vol. 181(C).
    3. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2020. "Mission abort policy optimization for series systems with overlapping primary and rescue subsystems operating in a random environment," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    4. Ji Hwan Cha & Maxim Finkelstein, 2020. "On optimal life extension for degrading systems," Journal of Risk and Reliability, , vol. 234(3), pages 487-495, June.
    5. Levitin, Gregory & Finkelstein, Maxim, 2018. "Optimal mission abort policy for systems in a random environment with variable shock rate," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 11-17.
    6. Maxim Finkelstein & Ji Hwan Cha, 2022. "Reducing degradation and age of items in imperfect repair modeling," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 1058-1081, December.
    7. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2018. "Mission abort policy balancing the uncompleted mission penalty and system loss risk," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 194-201.
    8. Finkelstein, Maxim & Ludick, Zani, 2014. "On some steady-state characteristics of systems with gradual repair," Reliability Engineering and System Safety, Elsevier, vol. 128(C), pages 17-23.
    9. Badía, Francisco German & Sangüesa, Carmen & Cha, Ji Hwan, 2018. "Stochastic comparisons and multivariate dependence for the epoch times of trend renewal processes," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 174-184.
    10. Cha, Ji Hwan & Finkelstein, Maxim, 2019. "Stochastic modeling for systems with delayed failures," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 118-124.
    11. Badía, F.G. & Berrade, M.D. & Cha, Ji Hwan & Lee, Hyunju, 2018. "Optimal replacement policy under a general failure and repair model: Minimal versus worse than old repair," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 362-372.
    12. Ji Hwan Cha & Massimiliano Giorgio, 2018. "Modelling of Marginally Regular Bivariate Counting Process and its Application to Shock Model," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1137-1154, December.
    13. Levitin, Gregory & Finkelstein, Maxim & Huang, Hong-Zhong, 2019. "Scheduling of imperfect inspections for reliability critical systems with shock-driven defects and delayed failures," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 89-98.
    14. Gregory Levitin & Maxim Finkelstein, 2018. "Optimal mission abort policy with multiple shock number thresholds," Journal of Risk and Reliability, , vol. 232(6), pages 607-615, December.
    15. Ji Hwan Cha & Maxim Finkelstein, 2019. "Optimal preventive maintenance for systems having a continuous output and operating in a random environment," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 327-350, July.
    16. Cha, Ji Hwan & Finkelstein, Maxim, 2014. "Some notes on unobserved parameters (frailties) in reliability modeling," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 99-103.
    17. Cha, Ji Hwan & Finkelstein, Maxim, 2016. "New shock models based on the generalized Polya process," European Journal of Operational Research, Elsevier, vol. 251(1), pages 135-141.
    18. Ji Hwan Cha & Maxim Finkelstein, 2018. "On a New Shot Noise Process and the Induced Survival Model," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 897-917, September.
    19. Sophie Mercier & Hai Ha Pham, 2016. "A Random Shock Model with Mixed Effect, Including Competing Soft and Sudden Failures, and Dependence," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 377-400, June.
    20. Levitin, Gregory & Finkelstein, Maxim & Huang, Hong-Zong, 2020. "Optimal mission abort policies for multistate systems," Reliability Engineering and System Safety, Elsevier, vol. 193(C).

    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:eee:jmvana:v:127:y:2014:i:c:p:151-159. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.