IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v101y2010i5p1311-1316.html
   My bibliography  Save this article

Expansions for the multivariate normal

Author

Listed:
  • Withers, Christopher S.
  • Nadarajah, Saralees

Abstract

Mehler gave an expansion for the standard bivariate normal density. Kibble extended it to a multivariate normal density whose covariance is a correlation matrix. We give extensions of these expansions for general covariances.

Suggested Citation

  • Withers, Christopher S. & Nadarajah, Saralees, 2010. "Expansions for the multivariate normal," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1311-1316, May.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:5:p:1311-1316
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(10)00007-2
    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. Kotz,Samuel & Nadarajah,Saralees, 2004. "Multivariate T-Distributions and Their Applications," Cambridge Books, Cambridge University Press, number 9780521826549.
    2. Withers, C. S., 2000. "A simple expression for the multivariate Hermite polynomials," Statistics & Probability Letters, Elsevier, vol. 47(2), pages 165-169, April.
    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. Dueck, Johannes & Edelmann, Dominic & Richards, Donald, 2017. "Distance correlation coefficients for Lancaster distributions," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 19-39.

    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. Wan-Lun Wang, 2019. "Mixture of multivariate t nonlinear mixed models for multiple longitudinal data with heterogeneity and missing values," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 196-222, March.
    2. Lamboni, Matieyendou, 2022. "Efficient dependency models: Simulating dependent random variables," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 199-217.
    3. Chen, Tao & Martin, Elaine & Montague, Gary, 2009. "Robust probabilistic PCA with missing data and contribution analysis for outlier detection," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3706-3716, August.
    4. Christopher S. Withers & Saralees Nadarajah, 2014. "Expansions about the Gamma for the Distribution and Quantiles of a Standard Estimate," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 693-713, September.
    5. Catania, Leopoldo & Proietti, Tommaso, 2020. "Forecasting volatility with time-varying leverage and volatility of volatility effects," International Journal of Forecasting, Elsevier, vol. 36(4), pages 1301-1317.
    6. Yuzhu Tian & Er’qian Li & Maozai Tian, 2016. "Bayesian joint quantile regression for mixed effects models with censoring and errors in covariates," Computational Statistics, Springer, vol. 31(3), pages 1031-1057, September.
    7. Jondeau, Eric, 2016. "Asymmetry in tail dependence in equity portfolios," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 351-368.
    8. Badi H. Baltagi & Georges Bresson & Anoop Chaturvedi & Guy Lacroix, 2022. "Robust Dynamic Space-Time Panel Data Models Using ε-contamination: An Application to Crop Yields and Climate Change," Center for Policy Research Working Papers 254, Center for Policy Research, Maxwell School, Syracuse University.
    9. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107034723.
    10. A. El-Bassiouny & M. Jones, 2009. "A bivariate F distribution with marginals on arbitrary numerator and denominator degrees of freedom, and related bivariate beta and t distributions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 18(4), pages 465-481, November.
    11. Punzo, Antonio & Bagnato, Luca, 2022. "Dimension-wise scaled normal mixtures with application to finance and biometry," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    12. Domínguez-Molina, J. Armando & Rocha-Arteaga, Alfonso, 2007. "On the infinite divisibility of some skewed symmetric distributions," Statistics & Probability Letters, Elsevier, vol. 77(6), pages 644-648, March.
    13. Paolella, Marc S. & Polak, Paweł, 2015. "ALRIGHT: Asymmetric LaRge-scale (I)GARCH with Hetero-Tails," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 282-297.
    14. Arismendi, J.C., 2013. "Multivariate truncated moments," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 41-75.
    15. Balakrishnan, N. & Hashorva, E., 2011. "On Pearson-Kotz Dirichlet distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 948-957, May.
    16. Nason, Guy P., 2006. "On the sum of t and Gaussian random variables," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1280-1286, July.
    17. Thomas Holgersson & Peter Karlsson & Andreas Stephan, 2020. "A risk perspective of estimating portfolio weights of the global minimum-variance portfolio," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(1), pages 59-80, March.
    18. Díaz-García, José A. & Gutiérrez-Jáimez, Ramón, 2006. "The distribution of the residual from a general elliptical multivariate linear model," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1829-1841, September.
    19. Torri, Gabriele & Giacometti, Rosella & Tichý, Tomáš, 2021. "Network tail risk estimation in the European banking system," Journal of Economic Dynamics and Control, Elsevier, vol. 127(C).
    20. Ñíguez, Trino-Manuel & Perote, Javier, 2016. "Multivariate moments expansion density: Application of the dynamic equicorrelation model," Journal of Banking & Finance, Elsevier, vol. 72(S), pages 216-232.

    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:101:y:2010:i:5:p:1311-1316. 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.