IDEAS home Printed from https://ideas.repec.org/a/vrs/demode/v4y2016i1p29n1.html
   My bibliography  Save this article

Exact distributions of order statistics of dependent random variables from ln,p-symmetric sample distributions, n ∈ {3,4}

Author

Listed:
  • Müller K.

    (University of Rostock, Institute of Mathematics, Ulmenstraße 69, Haus 3, 18057 Rostock, Germany)

  • Richter W.-D.

    (University of Rostock, Institute of Mathematics, Ulmenstraße 69, Haus 3, 18057 Rostock, Germany)

Abstract

Integral representations of the exact distributions of order statistics are derived in a geometric way when three or four random variables depend on each other as the components of continuous ln,psymmetrically distributed random vectors do, n ∈ {3,4}, p > 0. Once the representations are implemented in a computer program, it is easy to change the density generator of the ln,p-symmetric distribution with another one for newly evaluating the distribution of interest. For two groups of stock exchange index residuals, maximum distributions are compared under dependence and independence modeling.

Suggested Citation

  • Müller K. & Richter W.-D., 2016. "Exact distributions of order statistics of dependent random variables from ln,p-symmetric sample distributions, n ∈ {3,4}," Dependence Modeling, De Gruyter, vol. 4(1), pages 1-29, February.
    • Handle: RePEc:vrs:demode:v:4:y:2016:i:1:p:29:n:1
    DOI: 10.1515/demo-2016-0001
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/demo-2016-0001
    Download Restriction: no
    File URL: https://libkey.io/10.1515/demo-2016-0001?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
    ---><---

    References listed on IDEAS

    as
    1. Panayiotis Theodossiou, 1998. "Financial Data and the Skewed Generalized T Distribution," Management Science, INFORMS, vol. 44(12-Part-1), pages 1650-1661, December.
    2. Saralees Nadarajah, 2006. "Acknowledgement of Priority: the Generalized Normal Distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(9), pages 1031-1032.
    3. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2008. "On the exact distribution of the maximum of absolutely continuous dependent random variables," Statistics & Probability Letters, Elsevier, vol. 78(1), pages 27-35, January.
    4. Jamalizadeh, A. & Balakrishnan, N., 2010. "Distributions of order statistics and linear combinations of order statistics from an elliptical distribution as mixtures of unified skew-elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1412-1427, July.
    5. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2007. "On the exact distribution of linear combinations of order statistics from dependent random variables," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1876-1894, November.
    6. Saralees Nadarajah, 2005. "A generalized normal distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(7), pages 685-694.
    7. Klaus Müller & Wolf-Dieter Richter, 2015. "Exact extreme value, product, and ratio distributions under non-standard assumptions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(1), pages 1-30, January.
    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. Müller K. & Richter W.-D., 2016. "Extreme value distributions for dependent jointly ln,p-symmetrically distributed random variables," Dependence Modeling, De Gruyter, vol. 4(1), pages 1-33, February.
    2. Müller K. & Richter W.-D., 2017. "Exact distributions of order statistics from ln,p-symmetric sample distributions," Dependence Modeling, De Gruyter, vol. 5(1), pages 221-245, August.
    3. R. Arellano-Valle & Ahad Jamalizadeh & H. Mahmoodian & N. Balakrishnan, 2014. "$$L$$ L -statistics from multivariate unified skew-elliptical distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(4), pages 559-583, May.
    4. Madadi, Mohsen & Khalilpoor, Parisa & Jamalizadeh, Ahad, 2015. "Regression mean residual life of a system with three dependent components with normal lifetimes," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 182-191.
    5. Jamalizadeh, A. & Balakrishnan, N., 2010. "Distributions of order statistics and linear combinations of order statistics from an elliptical distribution as mixtures of unified skew-elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1412-1427, July.
    6. Tran, Quang Van & Kukal, Jaromir, 2022. "A novel heavy tail distribution of logarithmic returns of cryptocurrencies," Finance Research Letters, Elsevier, vol. 47(PA).
    7. Jamalizadeh, A. & Balakrishnan, N. & Salehi, Mehdi, 2010. "Order statistics and linear combination of order statistics arising from a bivariate selection normal distribution," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 445-451, March.
    8. Lui, Kung-Jong & Chang, Kuang-Chao, 2009. "Corrigendum to: "Testing homogeneity of risk difference in stratified randomized trials with noncompliance" [Comput. Statist. Data Anal. 53 (2008) 209-221]," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1529-1529, February.
    9. Jamalizadeh, A. & Mehrali, Y. & Balakrishnan, N., 2009. "Recurrence relations for bivariate t and extended skew-t distributions and an application to order statistics from bivariate t," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4018-4027, October.
    10. Klaus Müller & Wolf-Dieter Richter, 2015. "Exact extreme value, product, and ratio distributions under non-standard assumptions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(1), pages 1-30, January.
    11. Jamalizadeh, A. & Balakrishnan, N., 2009. "Prediction in a trivariate normal distribution via a linear combination of order statistics," Statistics & Probability Letters, Elsevier, vol. 79(21), pages 2289-2296, November.
    12. Mehdi Amiri & Yaser Mehrali & Narayanaswamy Balakrishnan & Ahad Jamalizadeh, 2022. "Efficient recursive computational algorithms for multivariate t and multivariate unified skew-t distributions with applications to inference," Computational Statistics, Springer, vol. 37(1), pages 125-158, March.
    13. Delis, Manthos & Savva, Christos & Theodossiou, Panayiotis, 2020. "A Coronavirus Asset Pricing Model: The Role of Skewness," MPRA Paper 100877, University Library of Munich, Germany.
    14. BenSaïda, Ahmed & Slim, Skander, 2016. "Highly flexible distributions to fit multiple frequency financial returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 203-213.
    15. G. D. Gettinby & C. D. Sinclair & D. M. Power & R. A. Brown, 2004. "An Analysis of the Distribution of Extreme Share Returns in the UK from 1975 to 2000," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 31(5‐6), pages 607-646, June.
    16. 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.
    17. Ellina, Polina & Mascarenhas, Briance & Theodossiou, Panayiotis, 2020. "Clarifying managerial biases using a probabilistic framework," Journal of Behavioral and Experimental Finance, Elsevier, vol. 27(C).
    18. Monica Billio & Ludovic Calès & Dominique Guegan, 2010. "A Cross-Sectional Performance Measure for Portfolio Management," Documents de travail du Centre d'Economie de la Sorbonne 10070, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    19. James Hansen & James McDonald & Panayiotis Theodossiou & Brad Larsen, 2010. "Partially Adaptive Econometric Methods For Regression and Classification," Computational Economics, Springer;Society for Computational Economics, vol. 36(2), pages 153-169, August.
    20. Kevin Fergusson & Eckhard Platen, 2006. "On the Distributional Characterization of Daily Log-Returns of a World Stock Index," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(1), pages 19-38.

    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:vrs:demode:v:4:y:2016:i:1:p:29:n:1. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.