IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v79y2009i16p1733-1743.html
   My bibliography  Save this article

Multivariate flexible Pareto model: Dependency structure, properties and characterizations

Author

Listed:
  • Chiragiev, Arthur
  • Landsman, Zinoviy

Abstract

The classical multivariate Pareto model, which was referred to by Arnold [Arnold, B.C., 1983. Pareto Distributions. International Co-operative Publishing House], and is used to fit heavy tailed random variables, has serious disadvantages. First, each of its marginals has the same distribution up to location and scale parameters. Secondly, this model has a rigid dependence structure. Furthermore, the independent Pareto marginals do not belong to this model. In this paper, we introduce two multivariate models, whose marginals have different shape parameters and a more flexible dependence structure. Moreover, the independent Pareto marginals model is a special case of one of the suggested models. We also discuss regression and a measure of dependence for these models, along with some relevant inferences. The paper concludes with a numerical study.

Suggested Citation

  • Chiragiev, Arthur & Landsman, Zinoviy, 2009. "Multivariate flexible Pareto model: Dependency structure, properties and characterizations," Statistics & Probability Letters, Elsevier, vol. 79(16), pages 1733-1743, August.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:16:p:1733-1743
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(09)00161-8
    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. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, October.
    2. Mathai, A. M. & Moschopoulos, P. G., 1991. "On a multivariate gamma," Journal of Multivariate Analysis, Elsevier, vol. 39(1), pages 135-153, October.
    3. Justel, Ana & Peña, Daniel & Zamar, Rubén, 1997. "A multivariate Kolmogorov-Smirnov test of goodness of fit," Statistics & Probability Letters, Elsevier, vol. 35(3), pages 251-259, October.
    4. Pycke, Jean-Renaud, 2003. "Multivariate extensions of the Anderson-Darling process," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 387-399, July.
    5. Justel, Ana & Peña, Daniel & Zamar, Rubén, 1997. "A multivariate Kolmogorov-Smirnov test of goodness of fit," Statistics & Probability Letters, Elsevier, vol. 35(3), pages 251-259, October.
    6. Paul Embrechts & Sidney Resnick & Gennady Samorodnitsky, 1999. "Extreme Value Theory as a Risk Management Tool," North American Actuarial Journal, Taylor & Francis Journals, vol. 3(2), pages 30-41.
    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. Sarabia, José María & Gómez-Déniz, Emilio & Prieto, Faustino & Jordá, Vanesa, 2016. "Risk aggregation in multivariate dependent Pareto distributions," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 154-163.
    2. Jianxi Su & Edward Furman, 2016. "A form of multivariate Pareto distribution with applications to financial risk measurement," Papers 1607.04737, arXiv.org.
    3. Jianxi Su & Edward Furman, 2016. "Multiple risk factor dependence structures: Distributional properties," Papers 1607.04739, arXiv.org.
    4. Su, Jianxi & Furman, Edward, 2017. "Multiple risk factor dependence structures: Distributional properties," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 56-68.
    5. José María Sarabia & Vanesa Jordá & Faustino Prieto & Montserrat Guillén, 2020. "Multivariate Classes of GB2 Distributions with Applications," Mathematics, MDPI, vol. 9(1), pages 1-21, December.
    6. Asimit, Alexandru V. & Furman, Edward & Vernic, Raluca, 2010. "On a multivariate Pareto distribution," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 308-316, April.

    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. Squalli, Jay, 2017. "Renewable energy, coal as a baseload power source, and greenhouse gas emissions: Evidence from U.S. state-level data," Energy, Elsevier, vol. 127(C), pages 479-488.
    2. Torri, Gabriele & Giacometti, Rosella & Paterlini, Sandra, 2018. "Robust and sparse banking network estimation," European Journal of Operational Research, Elsevier, vol. 270(1), pages 51-65.
    3. Langrené, Nicolas & Warin, Xavier, 2021. "Fast multivariate empirical cumulative distribution function with connection to kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 162(C).
    4. R. N. Rattihalli, 2023. "A Class of Multivariate Power Skew Symmetric Distributions: Properties and Inference for the Power-Parameter," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1356-1393, August.
    5. Zuliqar Ali & Ijaz Hussain & Muhammad Faisal & Hafiza Mamona Nazir & Mitwali Abd-el Moemen & Tajammal Hussain & Sadaf Shamsuddin, 2017. "A Novel Multi-Scalar Drought Index for Monitoring Drought: the Standardized Precipitation Temperature Index," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(15), pages 4957-4969, December.
    6. Jean-David Fermanian, 2003. "Goodness of Fit Tests for Copulas," Working Papers 2003-34, Center for Research in Economics and Statistics.
    7. Abul Kalam Azad & Mohammad Golam Rasul & Talal Yusaf, 2014. "Statistical Diagnosis of the Best Weibull Methods for Wind Power Assessment for Agricultural Applications," Energies, MDPI, vol. 7(5), pages 1-30, May.
    8. Audrius Kabašinskas & Leonidas Sakalauskas & Ingrida Vaičiulytė, 2021. "An Analytical EM Algorithm for Sub-Gaussian Vectors," Mathematics, MDPI, vol. 9(9), pages 1-20, April.
    9. Katarína Remeňová & Jakub Kintler & Nadežda Jankelová, 2020. "The General Concept of the Revenue Model for Sustainability Growth," Sustainability, MDPI, vol. 12(16), pages 1-12, August.
    10. Jason J. Sauppe & Sheldon H. Jacobson, 2017. "The role of covariate balance in observational studies," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(4), pages 323-344, June.
    11. Carolina Gil Marcelino & Carlos Camacho-Gómez & Silvia Jiménez-Fernández & Sancho Salcedo-Sanz, 2021. "Optimal Generation Scheduling in Hydro-Power Plants with the Coral Reefs Optimization Algorithm," Energies, MDPI, vol. 14(9), pages 1-24, April.
    12. Jun Wang & Shouhong Zhang & Yiping Guo, 2019. "Analyzing the Impact of Impervious Area Disconnection on Urban Runoff Control Using an Analytical Probabilistic Model," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(5), pages 1753-1768, March.
    13. Knyazev, Alexander & Lepekhin, Oleg & Shemyakin, Arkady, 2016. "Joint distribution of stock indices: Methodological aspects of construction and selection of copula models," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 42, pages 30-53.
    14. Fermanian, Jean-David, 2005. "Goodness-of-fit tests for copulas," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 119-152, July.
    15. Morteza Amini & Nader Nematollahi, 2017. "Estimation of the Parameters of a Selected Multivariate Population," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(1), pages 13-38, February.
    16. Petrie, Adam & Willemain, Thomas R., 2013. "An empirical study of tests for uniformity in multidimensional data," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 253-268.
    17. Jin Zhang & Yuehua Wu, 2002. "Beta Approximation to the Distribution of Kolmogorov-Smirnov Statistic," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(3), pages 577-584, September.
    18. Li, Johnny Siu-Hang & Liu, Yanxin & Chan, Wai-Sum, 2023. "Hedging longevity risk under non-Gaussian state-space stochastic mortality models: A mean-variance-skewness-kurtosis approach," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 96-121.
    19. Farzin Golzar & David Nilsson & Viktoria Martin, 2020. "Forecasting Wastewater Temperature Based on Artificial Neural Network (ANN) Technique and Monte Carlo Sensitivity Analysis," Sustainability, MDPI, vol. 12(16), pages 1-17, August.
    20. Psaradakis, Zacharias & Vávra, Marián, 2017. "A distance test of normality for a wide class of stationary processes," Econometrics and Statistics, Elsevier, vol. 2(C), pages 50-60.

    More about this item

    Statistics

    Access and download statistics

    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:stapro:v:79:y:2009:i:16:p:1733-1743. 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.