IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v101y2010i3p491-499.html
   My bibliography  Save this article

A multivariate extension of Sarhan and Balakrishnan's bivariate distribution and its ageing and dependence properties

Author

Listed:
  • Franco, Manuel
  • Vivo, Juana-María

Abstract

A new class of bivariate distributions (NBD) was recently introduced by Sarhan and Balakrishnan [A.M. Sarhan, N. Balakrishnan, A new class of bivariate distributions and its mixture, J. Multivariate Anal. 98 (2007) 1508-1527]. In this note, we give the joint survival function of a multivariate extension of the NBD, which is not an absolutely continuous multivariate distribution, and its marginal and extreme order statistics distributions are also derived. The multivariate ageing and dependence properties of the proposed n-dimensional distribution are also discussed, and then we analyze the stochastic ageing of its marginals and its minimum and maximum order statistics.

Suggested Citation

  • Franco, Manuel & Vivo, Juana-María, 2010. "A multivariate extension of Sarhan and Balakrishnan's bivariate distribution and its ageing and dependence properties," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 491-499, March.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:3:p:491-499
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(09)00149-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Nadarajah, Saralees, 2008. "Letter to the editor," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 574-575, March.
    2. Nadarajah, Saralees, 2008. "Letter to the Editor," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 1010-1012, May.
    3. Nadarajah, Saralees & Kotz, Samuel, 2008. "Letter to the Editor," Journal of Multivariate Analysis, Elsevier, vol. 99(2), pages 306-307, February.
    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. Boland, Philip J. & Hollander, Myles & Joag-Dev, Kumar & Kochar, Subhash, 1996. "Bivariate Dependence Properties of Order Statistics," Journal of Multivariate Analysis, Elsevier, vol. 56(1), pages 75-89, January.
    6. Colangelo, Antonio & Hu, Taizhong & Shaked, Moshe, 2008. "Conditional orderings and positive dependence," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 358-371, March.
    7. Colangelo, Antonio & Scarsini, Marco & Shaked, Moshe, 2005. "Some notions of multivariate positive dependence," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 13-26, August.
    8. Saralees Nadarajah, 2008. "Reply to the letter to the editor," Computational Statistics, Springer, vol. 23(4), pages 667-668, October.
    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. Manuel Franco & Juana-María Vivo & Debasis Kundu, 2020. "A Generator of Bivariate Distributions: Properties, Estimation, and Applications," Mathematics, MDPI, vol. 8(10), pages 1-30, October.
    2. Mehdi Basikhasteh & Iman Makhdoom, 2022. "Bayesian inference of bivariate Weibull geometric model based on LINEX and quadratic loss functions," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(2), pages 867-880, April.
    3. Muhammad Mohsin & Hannes Kazianka & Jürgen Pilz & Albrecht Gebhardt, 2014. "A new bivariate exponential distribution for modeling moderately negative dependence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(1), pages 123-148, March.
    4. Kundu, Debasis & Gupta, Arjun K., 2014. "On bivariate Weibull-Geometric distribution," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 19-29.

    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. Ali Genç, 2013. "Moments of truncated normal/independent distributions," Statistical Papers, Springer, vol. 54(3), pages 741-764, August.
    2. Kundu, Debasis & Franco, Manuel & Vivo, Juana-Maria, 2014. "Multivariate distributions with proportional reversed hazard marginals," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 98-112.
    3. Ori Davidov & Amir Herman, 2011. "Multivariate Stochastic Orders Induced by Case-Control Sampling," Methodology and Computing in Applied Probability, Springer, vol. 13(1), pages 139-154, March.
    4. Cai, Jun & Wei, Wei, 2012. "Optimal reinsurance with positively dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 57-63.
    5. Gijbels, Irène & Sznajder, Dominik, 2013. "Testing tail monotonicity by constrained copula estimation," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 338-351.
    6. Colangelo Antonio, 2005. "Multivariate hazard orderings of discrete random vectors," Economics and Quantitative Methods qf05010, Department of Economics, University of Insubria.
    7. Zhuang, Weiwei & Yao, Junchao & Hu, Taizhong, 2010. "Conditional ordering of order statistics," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 640-644, March.
    8. García, V.J. & Gómez-Déniz, E. & Vázquez-Polo, F.J., 2010. "A new skew generalization of the normal distribution: Properties and applications," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 2021-2034, August.
    9. Lu, Zhiyi & Meng, Shengwang & Liu, Leping & Han, Ziqi, 2018. "Optimal insurance design under background risk with dependence," Insurance: Mathematics and Economics, Elsevier, vol. 80(C), pages 15-28.
    10. Arnold Polanski & Evarist Stoja & Ching‐Wai (Jeremy) Chiu, 2021. "Tail risk interdependence," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(4), pages 5499-5511, October.
    11. 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.
    12. Alexander Saak, 2007. "A note on the value of public information in monopoly," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(2), pages 369-379, November.
    13. Calabrese, Raffaella & Osmetti, Silvia Angela, 2019. "A new approach to measure systemic risk: A bivariate copula model for dependent censored data," European Journal of Operational Research, Elsevier, vol. 279(3), pages 1053-1064.
    14. Elina Robeva & Bernd Sturmfels & Ngoc Tran & Caroline Uhler, 2021. "Maximum likelihood estimation for totally positive log‐concave densities," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 817-844, September.
    15. Smith, James L. & Thompson, Rex, 2009. "Rational plunging and the option value of sequential investment: The case of petroleum exploration," The Quarterly Review of Economics and Finance, Elsevier, vol. 49(3), pages 1009-1033, August.
    16. Surya, Budhi Arta, 2022. "Conditional multivariate distributions of phase-type for a finite mixture of Markov jump processes given observations of sample path," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    17. Indranil Ghosh & Osborne Banks, 2021. "A Study of Bivariate Generalized Pareto Distribution and its Dependence Structure Among Model Parameters," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 575-604, November.
    18. S. Ashrafi & M. Asadi, 2015. "On the stochastic and dependence properties of the three-state systems," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(3), pages 261-281, April.
    19. Cai, Jun & Wei, Wei, 2012. "On the invariant properties of notions of positive dependence and copulas under increasing transformations," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 43-49.
    20. Enrique de Amo & María del Rosario Rodríguez-Griñolo & Manuel Úbeda-Flores, 2024. "Directional Dependence Orders of Random Vectors," Mathematics, MDPI, vol. 12(3), pages 1-14, January.

    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:101:y:2010:i:3:p:491-499. 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.