IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i13p1505-d583281.html
   My bibliography  Save this article

A Variant of the Necessary Condition for the Absolute Continuity of Symmetric Multivariate Mixture

Author

Listed:
  • Evgeniy Anatolievich Savinov

    (Financial University under the Government of the Russian Federation, 125993 Moscow, Russia
    Current address: 49 Leningradsky Prospekt, GSP-3.)

Abstract

Sufficient conditions are given under which the absolute continuity of the joint distribution of conditionally independent random variables can be violated. It is shown that in the case of a dimension n > 1 this occurs for a sufficiently large number of discontinuity points of one-dimensional conditional distributions.

Suggested Citation

  • Evgeniy Anatolievich Savinov, 2021. "A Variant of the Necessary Condition for the Absolute Continuity of Symmetric Multivariate Mixture," Mathematics, MDPI, vol. 9(13), pages 1-3, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:13:p:1505-:d:583281
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/13/1505/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/13/1505/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Moshe Shaked & Fabio Spizzichino, 1998. "Positive Dependence Properties of Conditionally Independent Random Lifetimes," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 944-959, November.
    2. Belzunce, Félix & Mercader, José-Angel & Ruiz, José-María & Spizzichino, Fabio, 2009. "Stochastic comparisons of multivariate mixture models," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1657-1669, September.
    3. Baha-Eldin Khaledi & Subhash Kochar, 2001. "Dependence Properties of Multivariate Mixture Distributions and Their Applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(3), pages 620-630, September.
    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. Belzunce, Félix & Mercader, José-Angel & Ruiz, José-María & Spizzichino, Fabio, 2009. "Stochastic comparisons of multivariate mixture models," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1657-1669, September.
    2. Li, Xiaohu & Da, Gaofeng, 2010. "Stochastic comparisons in multivariate mixed model of proportional reversed hazard rate with applications," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 1016-1025, April.
    3. Ingvild M. Helgøy & Hans J. Skaug, 2022. "The Sibling Distribution for Multivariate Life Time Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 340-363, May.
    4. Xiaohu Li & Gaofeng Da & Peng Zhao, 2012. "Competing Between Two Groups of Individuals Following Frailty Models," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 1033-1051, December.
    5. Khaledi, Baha-Eldin & Shaked, Moshe, 2010. "Stochastic comparisons of multivariate mixtures," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2486-2498, November.
    6. Michel Denuit & Esther Frostig & Benny Levikson, 2007. "Supermodular Comparison of Time-to-Ruin Random Vectors," Methodology and Computing in Applied Probability, Springer, vol. 9(1), pages 41-54, March.
    7. Badía, F.G. & Sangüesa, C. & Cha, J.H., 2014. "Stochastic comparison of multivariate conditionally dependent mixtures," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 82-94.
    8. Spizzichino, F. & Torrisi, G. L., 2001. "Multivariate negative aging in an exchangeable model of heterogeneity," Statistics & Probability Letters, Elsevier, vol. 55(1), pages 71-82, November.
    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. Xiaoliang Ling & Ping Li, 2013. "Stochastic comparisons for the number of working components of a system in random environment," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(8), pages 1017-1030, November.
    11. S. Goli & M. Asadi, 2017. "A study on the conditional inactivity time of coherent systems," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(2), pages 227-241, February.
    12. Balakrishnan, Narayanaswamy & Barmalzan, Ghobad & Haidari, Abedin, 2016. "Multivariate stochastic comparisons of multivariate mixture models and their applications," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 37-43.
    13. Michel Denuit, 2009. "Life Anuities with Stochastic Survival Probabilities: A Review," Methodology and Computing in Applied Probability, Springer, vol. 11(3), pages 463-489, September.
    14. Alfred Müller & Marco Scarsini, 2001. "Stochastic Comparison of Random Vectors with a Common Copula," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 723-740, November.
    15. Bezgina, E. & Burkschat, M., 2019. "On total positivity of exchangeable random variables obtained by symmetrization, with applications to failure-dependent lifetimes," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 95-109.
    16. Zhao, Peng & Balakrishnan, N., 2009. "Stochastic comparison and monotonicity of inactive record values," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 566-572, March.
    17. Burkschat, M., 2009. "Multivariate dependence of spacings of generalized order statistics," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1093-1106, July.
    18. Francisco Germán Badía & Hyunju Lee, 2020. "On stochastic comparisons and ageing properties of multivariate proportional hazard rate mixtures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(3), pages 355-375, April.
    19. Somayeh Zarezadeh & Somayeh Ashrafi & Majid Asadi, 2018. "Network Reliability Modeling Based on a Geometric Counting Process," Mathematics, MDPI, vol. 6(10), pages 1-17, October.
    20. Francesco Buono & Emilio Santis & Maria Longobardi & Fabio Spizzichino, 2022. "Multivariate Reversed Hazard Rates and Inactivity Times of Systems," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1987-2008, 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:gam:jmathe:v:9:y:2021:i:13:p:1505-:d:583281. 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.