IDEAS home Printed from https://ideas.repec.org/a/spr/sankhb/v83y2021i2d10.1007_s13571-020-00224-z.html
   My bibliography  Save this article

A Study of Bivariate Generalized Pareto Distribution and its Dependence Structure Among Model Parameters

Author

Listed:
  • Indranil Ghosh

    (University of North Carolina)

  • Osborne Banks

    (University of North Carolina)

Abstract

Several variants of the classical bivariate and multivariate generalized Pareto distributions have been discussed and studied in the literature (see Arnold (1983, Stat. Prob. Lett. 17: 361–368, 1993, 2015), Arnold and Laguna (1977), Ali and Nadarajah (2007), Rootzen and Tajvidi (2006) and the references cited therein). Ali and Nadarajah (2007) studied a truncated version of the most popular long-tailed generalized bivariate Pareto distribution (GBPD, henceforth, in short) involving six parameters. However, not much discussion exists in the current literature on the structural properties as well as on the dependence structure among the parameters in this model. In this paper we re-visit the GBPD and discuss several other new properties. In addition, we study the shape of GBPD for varying choices of the model parameters and subsequently study their interdependence. Also, we provide copula based construction of GBPD and discuss the associated local dependence measures.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sankhb:v:83:y:2021:i:2:d:10.1007_s13571-020-00224-z
    DOI: 10.1007/s13571-020-00224-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13571-020-00224-z
    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/s13571-020-00224-z?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. P. G. Sankaran & N. Unnikrishnan Nair & Preethi John, 2014. "A family of bivariate Pareto distributions," Statistica, Department of Statistics, University of Bologna, vol. 74(2), pages 199-215.
    2. Arnold, Barry C. & Castillo, Enrique & Sarabia, Jose María, 1993. "Multivariate distributions with generalized Pareto conditionals," Statistics & Probability Letters, Elsevier, vol. 17(5), pages 361-368, August.
    3. Joe, Harry, 2005. "Asymptotic efficiency of the two-stage estimation method for copula-based models," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 401-419, June.
    4. Colangelo, Antonio & Hu, Taizhong & Shaked, Moshe, 2008. "Conditional orderings and positive dependence," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 358-371, March.
    5. Jones, M. C., 1998. "Constant Local Dependence," Journal of Multivariate Analysis, Elsevier, vol. 64(2), pages 148-155, February.
    6. Falk, Michael & Guillou, Armelle, 2008. "Peaks-over-threshold stability of multivariate generalized Pareto distributions," Journal of Multivariate Analysis, Elsevier, vol. 99(4), pages 715-734, April.
    7. Johnson, N. L. & Kotz, Samuel, 1975. "A vector multivariate hazard rate," Journal of Multivariate Analysis, Elsevier, vol. 5(1), pages 53-66, March.
    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. Gupta, Ramesh C., 2001. "Reliability Studies of Bivariate Distributions with Pareto Conditionals," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 214-225, February.
    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. Ramesh C. Gupta, 2006. "Reliability studies of bivariate distributions with Pearson type VII conditionals," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 239-251.
    4. Ramesh Gupta, 2011. "Bivariate odds ratio and association measures," Statistical Papers, Springer, vol. 52(1), pages 125-138, February.
    5. A. James & N. Chandra & Nicy Sebastian, 2023. "Stress-strength reliability estimation for bivariate copula function with rayleigh marginals," 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. 14(1), pages 196-215, March.
    6. J. Navarro & M. Esna-Ashari & M. Asadi & J. Sarabia, 2015. "Bivariate distributions with conditionals satisfying the proportional generalized odds rate model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(6), pages 691-709, August.
    7. Colangelo Antonio, 2005. "Multivariate hazard orderings of discrete random vectors," Economics and Quantitative Methods qf05010, Department of Economics, University of Insubria.
    8. Bouteska, Ahmed & Sharif, Taimur & Abedin, Mohammad Zoynul, 2023. "COVID-19 and stock returns: Evidence from the Markov switching dependence approach," Research in International Business and Finance, Elsevier, vol. 64(C).
    9. Hamza, Taher & Ben Haj Hamida, Hayet & Mili, Mehdi & Sami, Mina, 2024. "High inflation during Russia–Ukraine war and financial market interaction: Evidence from C-Vine Copula and SETAR models," Research in International Business and Finance, Elsevier, vol. 70(PB).
    10. Michael S. Smith & Shaun P. Vahey, 2016. "Asymmetric Forecast Densities for U.S. Macroeconomic Variables from a Gaussian Copula Model of Cross-Sectional and Serial Dependence," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 416-434, July.
    11. Jolani, Shahab, 2014. "An analysis of longitudinal data with nonignorable dropout using the truncated multivariate normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 163-173.
    12. Wang, Mengjiao & Liu, Jianxu & Yang, Bing, 2024. "Does the strength of the US dollar affect the interdependence among currency exchange rates of RCEP and CPTPP countries?," Finance Research Letters, Elsevier, vol. 62(PA).
    13. Li, Feng & Kang, Yanfei, 2018. "Improving forecasting performance using covariate-dependent copula models," International Journal of Forecasting, Elsevier, vol. 34(3), pages 456-476.
    14. Kojadinovic, Ivan & Yan, Jun, 2010. "Comparison of three semiparametric methods for estimating dependence parameters in copula models," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 52-63, August.
    15. N. Nair & P. Sankaran, 2014. "Modelling lifetimes with bivariate Schur-constant equilibrium distributions from renewal theory," METRON, Springer;Sapienza Università di Roma, vol. 72(3), pages 331-349, October.
    16. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    17. Kolev, Nikolai, 2016. "Characterizations of the class of bivariate Gompertz distributions," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 173-179.
    18. M. Shafaei Noughabi & M. Kayid, 2019. "Bivariate quantile residual life: a characterization theorem and statistical properties," Statistical Papers, Springer, vol. 60(6), pages 2001-2012, December.
    19. Ojea-Ferreiro, Javier & Reboredo, Juan C., 2022. "Exchange rates and the global transmission of equity market shocks," Economic Modelling, Elsevier, vol. 114(C).
    20. Corduas, Marcella, 2015. "A statistical model for consumer preferences: the case of Italian extra virgin olive oil," 143rd Joint EAAE/AAEA Seminar, March 25-27, 2015, Naples, Italy 202701, European Association of Agricultural Economists.

    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:sankhb:v:83:y:2021:i:2:d:10.1007_s13571-020-00224-z. 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.