IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v10y1980i2p207-232.html
   My bibliography  Save this article

Class L of multivariate distributions and its subclasses

Author

Listed:
  • Sato, Ken-iti

Abstract

For any class Q of distributions on Rd, let (Q) be the class of limit distributions of bn-1(X1 + ... + Xn) - an, where {Xn} are independent Rd-valued random variables, each with distribution in Q, bn > 0, an [set membership, variant] Rd, and {bn-1Xj} is a null array. When Q is the class of all distributions on Rd. (Q) = L0 is the usual class L. Define Lm = (Lm-1) and L[infinity] = [intersection]Lm. It is shown that this definition of Lm is equivalent to Urbanik's definition. Description of Lévy measures and representation of characteristic functions of members in these classes are given. Other characterizations of the class L[infinity] are made. Conditions for convergence in terms of the representations are given. Continuity properties of distributions of class L are studied.

Suggested Citation

  • Sato, Ken-iti, 1980. "Class L of multivariate distributions and its subclasses," Journal of Multivariate Analysis, Elsevier, vol. 10(2), pages 207-232, June.
    • Handle: RePEc:eee:jmvana:v:10:y:1980:i:2:p:207-232
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0047-259X(80)90014-7
    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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jurek, Zbigniew J., 2023. "Which Urbanik class Lk, do the hyperbolic and the generalized logistic characteristic functions belong to?," Statistics & Probability Letters, Elsevier, vol. 197(C).
    2. Akita, Koji & Maejima, Makoto, 2002. "On certain self-decomposable self-similar processes with independent increments," Statistics & Probability Letters, Elsevier, vol. 59(1), pages 53-59, August.
    3. Maejima, Makoto & Sato, Ken-iti & Watanabe, Toshiro, 2000. "Distributions of selfsimilar and semi-selfsimilar processes with independent increments," Statistics & Probability Letters, Elsevier, vol. 47(4), pages 395-401, May.
    4. Buchmann, Boris & Lu, Kevin W. & Madan, Dilip B., 2020. "Self-decomposability of weak variance generalised gamma convolutions," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 630-655.
    5. Cohen, Serge & Maejima, Makoto, 2011. "Selfdecomposability of moving average fractional Lévy processes," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1664-1669, November.
    6. Pérez-Abreu, Victor & Stelzer, Robert, 2014. "Infinitely divisible multivariate and matrix Gamma distributions," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 155-175.
    7. Rajba, Teresa, 2009. "Nested classes of C-semi-selfdecomposable distributions," Statistics & Probability Letters, Elsevier, vol. 79(24), pages 2469-2475, December.
    8. Chi, Yichun & Yang, Jingping & Qi, Yongcheng, 2009. "Decomposition of a Schur-constant model and its applications," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 398-408, June.

    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:10:y:1980:i:2:p:207-232. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.