IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v37y1998i3p213-221.html
   My bibliography  Save this article

Mixture representations for symmetric generalized Linnik laws

Author

Listed:
  • Pakes, Anthony G.

Abstract

This paper offers a simple proof based on random variable representations for a mixture representation of symmetric Linnik laws previously derived by purely analytic means. The new approach can be set in a much more general context which embraces the symmetric and the positive generalized Linnik laws.

Suggested Citation

  • Pakes, Anthony G., 1998. "Mixture representations for symmetric generalized Linnik laws," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 213-221, March.
    • Handle: RePEc:eee:stapro:v:37:y:1998:i:3:p:213-221
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(97)00119-3
    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. Kotz, Samuel & Ostrovskii, I. V., 1996. "A mixture representation of the Linnik distribution," Statistics & Probability Letters, Elsevier, vol. 26(1), pages 61-64, January.
    2. R. Pillai, 1990. "On Mittag-Leffler functions and related distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(1), pages 157-161, March.
    3. Devroye, Luc, 1990. "A note on linnik's distribution," Statistics & Probability Letters, Elsevier, vol. 9(4), pages 305-306, 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. Lekshmi, V. Seetha & Jose, K.K., 2006. "Autoregressive processes with Pakes and geometric Pakes generalized Linnik marginals," Statistics & Probability Letters, Elsevier, vol. 76(3), pages 318-326, February.
    2. Halvarsson, Daniel, 2013. "On the Estimation of Skewed Geometric Stable Distributions," Ratio Working Papers 216, The Ratio Institute.
    3. Dexter Cahoy, 2012. "An estimation procedure for the Linnik distribution," Statistical Papers, Springer, vol. 53(3), pages 617-628, August.
    4. Yury Khokhlov & Victor Korolev & Alexander Zeifman, 2020. "Multivariate Scale-Mixed Stable Distributions and Related Limit Theorems," Mathematics, MDPI, vol. 8(5), pages 1-29, May.
    5. Ashis SenGupta & Moumita Roy, 2023. "Circular-Statistics-Based Estimators and Tests for the Index Parameter α of Distributions for High-Volatility Financial Markets," JRFM, MDPI, vol. 16(9), pages 1-14, September.
    6. Jose, K.K. & Tomy, Lishamol & Sreekumar, J., 2008. "Autoregressive processes with normal-Laplace marginals," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2456-2462, October.

    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. Kozubowski, Tomasz J., 1998. "Mixture representation of Linnik distribution revisited," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 157-160, June.
    2. Yury Khokhlov & Victor Korolev & Alexander Zeifman, 2020. "Multivariate Scale-Mixed Stable Distributions and Related Limit Theorems," Mathematics, MDPI, vol. 8(5), pages 1-29, May.
    3. Dexter Cahoy, 2012. "An estimation procedure for the Linnik distribution," Statistical Papers, Springer, vol. 53(3), pages 617-628, August.
    4. Pakes, Anthony G., 1995. "Characterization of discrete laws via mixed sums and Markov branching processes," Stochastic Processes and their Applications, Elsevier, vol. 55(2), pages 285-300, February.
    5. Halvarsson, Daniel, 2013. "On the Estimation of Skewed Geometric Stable Distributions," Ratio Working Papers 216, The Ratio Institute.
    6. Ludwig Baringhaus & Rudolf Grübel, 1997. "On a Class of Characterization Problems for Random Convex Combinations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(3), pages 555-567, September.
    7. Yury Khokhlov & Victor Korolev, 2021. "On a Multivariate Analog of the Zolotarev Problem," Mathematics, MDPI, vol. 9(15), pages 1-20, July.
    8. Jose, K.K. & Tomy, Lishamol & Sreekumar, J., 2008. "Autoregressive processes with normal-Laplace marginals," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2456-2462, October.
    9. Cirillo, Pasquale & Hüsler, Jürg, 2009. "An urn approach to generalized extreme shock models," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 969-976, April.
    10. Browne, Sid & Bunge, John, 1995. "Random record processes and state dependent thinning," Stochastic Processes and their Applications, Elsevier, vol. 55(1), pages 131-142, January.
    11. Cho, Soobin & Kim, Panki, 2021. "Estimates on transition densities of subordinators with jumping density decaying in mixed polynomial orders," Stochastic Processes and their Applications, Elsevier, vol. 139(C), pages 229-279.
    12. Kozubowski, Tomasz J. & Meerschaert, Mark M., 2009. "A bivariate infinitely divisible distribution with exponential and Mittag-Leffler marginals," Statistics & Probability Letters, Elsevier, vol. 79(14), pages 1596-1601, July.
    13. Atangana, Abdon & Gómez-Aguilar, J.F., 2018. "Fractional derivatives with no-index law property: Application to chaos and statistics," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 516-535.
    14. Pillai, R. N. & Jayakumar, K., 1995. "Discrete Mittag-Leffler distributions," Statistics & Probability Letters, Elsevier, vol. 23(3), pages 271-274, May.
    15. Agahi, Hamzeh & Khalili, Monavar, 2020. "Truncated Mittag-Leffler distribution and superstatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    16. Tomasz Kozubowski, 2000. "Exponential Mixture Representation of Geometric Stable Distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(2), pages 231-238, June.
    17. Christoph, Gerd & Schreiber, Karina, 2000. "Scaled Sibuya distribution and discrete self-decomposability," Statistics & Probability Letters, Elsevier, vol. 48(2), pages 181-187, June.
    18. Sapatinas, Theofanis, 1995. "Characterizations of probability distributions based on discrete p-monotonicity," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 339-344, September.
    19. Agahi, Hamzeh & Alipour, Mohsen, 2019. "Mittag-Leffler-Gaussian distribution: Theory and application to real data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 156(C), pages 227-235.
    20. Zhang, Zhehao, 2018. "Renewal sums under mixtures of exponentials," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 281-301.

    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:37:y:1998:i:3:p:213-221. 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.