IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v95y2005i2p323-344.html
   My bibliography  Save this article

A new construction for skew multivariate distributions

Author

Listed:
  • Dey, Dipak K.
  • Liu, Junfeng

Abstract

This paper considers a new approach to develop a very general class of skew multivariate distributions. The approach is based on a linear combination of an elliptically distributed random variable with a linear constraint. Using this approach two different classes of multivariate distributions are constructed based on original distribution. These new classes include different types of skew normal (type A and type B) and other skew elliptical distributions, exist in the literature. We also derive the moment generating function, marginal and conditional density of our proposed classes of distributions. Straightforward explanations are applied to demonstrate the relationships among previous approaches by others with our proposed class of skew distributions.

Suggested Citation

  • Dey, Dipak K. & Liu, Junfeng, 2005. "A new construction for skew multivariate distributions," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 323-344, August.
    • Handle: RePEc:eee:jmvana:v:95:y:2005:i:2:p:323-344
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(04)00173-3
    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. Barry Arnold & Robert Beaver & A. Azzalini & N. Balakrishnan & A. Bhaumik & D. Dey & C. Cuadras & J. Sarabia & Barry Arnold & Robert Beaver, 2002. "Skewed multivariate models related to hidden truncation and/or selective reporting," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(1), pages 7-54, June.
    2. Barry Arnold & Robert Beaver & Richard Groeneveld & William Meeker, 1993. "The nontruncated marginal of a truncated bivariate normal distribution," Psychometrika, Springer;The Psychometric Society, vol. 58(3), pages 471-488, September.
    3. Liseo, Brunero & Loperfido, Nicola, 2003. "A Bayesian interpretation of the multivariate skew-normal distribution," Statistics & Probability Letters, Elsevier, vol. 61(4), pages 395-401, February.
    4. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    5. Branco, Márcia D. & Dey, Dipak K., 2001. "A General Class of Multivariate Skew-Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 99-113, 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. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility," Microeconomics Working Papers 22058, East Asian Bureau of Economic Research.
    2. Siddhartha Chib & Yasuhiro Omori & Manabu Asai, 2007. "Multivariate stochastic volatility (Revised in May 2007, Handbook of Financial Time Series (Published in "Handbook of Financial Time Series" (eds T.G. Andersen, R.A. Davis, Jens-Peter Kreiss," CARF F-Series CARF-F-094, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    3. Sreenivasa Rao Jammalamadaka & Emanuele Taufer & Gyorgy H. Terdik, 2021. "On Multivariate Skewness and Kurtosis," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 607-644, August.

    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. Sharon Lee & Geoffrey McLachlan, 2013. "On mixtures of skew normal and skew $$t$$ -distributions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 7(3), pages 241-266, September.
    2. Kim, Hyoung-Moon & Ryu, Duchwan & Mallick, Bani K. & Genton, Marc G., 2014. "Mixtures of skewed Kalman filters," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 228-251.
    3. Sharon Lee & Geoffrey McLachlan, 2013. "Model-based clustering and classification with non-normal mixture distributions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(4), pages 427-454, November.
    4. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2005. "On fundamental skew distributions," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 93-116, September.
    5. Young, Phil D. & Harvill, Jane L. & Young, Dean M., 2016. "A derivation of the multivariate singular skew-normal density function," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 40-45.
    6. Antonio Canale & Euloge Clovis Kenne Pagui & Bruno Scarpa, 2016. "Bayesian modeling of university first-year students' grades after placement test," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(16), pages 3015-3029, December.
    7. Hok Shing Kwong & Saralees Nadarajah, 2022. "A New Robust Class of Skew Elliptical Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1669-1691, September.
    8. Ley, Christophe & Paindaveine, Davy, 2010. "On the singularity of multivariate skew-symmetric models," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1434-1444, July.
    9. M. C. Jones, 2015. "On Families of Distributions with Shape Parameters," International Statistical Review, International Statistical Institute, vol. 83(2), pages 175-192, August.
    10. Azzalini, Adelchi, 2022. "An overview on the progeny of the skew-normal family— A personal perspective," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    11. V. G. Cancho & Reiko Aoki & V. H. Lachos, 2008. "Bayesian analysis for a skew extension of the multivariate null intercept measurement error model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(11), pages 1239-1251.
    12. Jose T.A.S. Ferreira & Mark F.J. Steel, 2004. "Bayesian Multivariate Regression Analysis with a New Class of Skewed Distributions," Econometrics 0403001, University Library of Munich, Germany.
    13. Panagiotelis, Anastasios & Smith, Michael, 2010. "Bayesian skew selection for multivariate models," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1824-1839, July.
    14. Zinoviy Landsman & Udi Makov & Tomer Shushi, 2017. "Extended Generalized Skew-Elliptical Distributions and their Moments," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(1), pages 76-100, February.
    15. Hossein Negarestani & Ahad Jamalizadeh & Sobhan Shafiei & Narayanaswamy Balakrishnan, 2019. "Mean mixtures of normal distributions: properties, inference and application," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(4), pages 501-528, May.
    16. Dylan Molenaar & Conor Dolan & Paul Boeck, 2012. "The Heteroscedastic Graded Response Model with a Skewed Latent Trait: Testing Statistical and Substantive Hypotheses Related to Skewed Item Category Functions," Psychometrika, Springer;The Psychometric Society, vol. 77(3), pages 455-478, July.
    17. Young, Phil D. & Kahle, David J. & Young, Dean M., 2017. "On the independence of singular multivariate skew-normal sub-vectors," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 58-62.
    18. Sreenivasa Rao Jammalamadaka & Emanuele Taufer & Gyorgy H. Terdik, 2021. "On Multivariate Skewness and Kurtosis," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 607-644, August.
    19. Kozubowski, Tomasz J. & Nolan, John P., 2008. "Infinite divisibility of skew Gaussian and Laplace laws," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 654-660, April.
    20. Hea-Jung Kim, 2015. "Segmented classification analysis with a class of rectangle-screened elliptical populations," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(9), pages 1877-1895, 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:eee:jmvana:v:95:y:2005:i:2:p:323-344. 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.