IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v107y2015icp145-149.html
   My bibliography  Save this article

On the Matsumoto–Yor type regression characterization of the gamma and Kummer distributions

Author

Listed:
  • Wesołowski, Jacek

Abstract

In this paper we study a Matsumoto–Yor type property for the gamma and Kummer independent variables discovered by Koudou and Vallois (2012). We prove that constancy of regressions of U=(1+(X+Y)−1)/(1+X−1) given V=X+Y and of U−1 given V, where X and Y are independent and positive random variables, characterizes the gamma and Kummer distributions. This result completes characterizations by independence of U and V obtained, under smoothness assumptions for densities, in Koudou and Vallois (2011, 2012). Since we work with differential equations for the Laplace transforms, no density assumptions are needed.

Suggested Citation

  • Wesołowski, Jacek, 2015. "On the Matsumoto–Yor type regression characterization of the gamma and Kummer distributions," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 145-149.
    • Handle: RePEc:eee:stapro:v:107:y:2015:i:c:p:145-149
    DOI: 10.1016/j.spl.2015.07.036
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715215002771
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2015.07.036?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
    ---><---

    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. Chou, Chao-Wei & Huang, Wen-Jang, 2004. "On characterizations of the gamma and generalized inverse Gaussian distributions," Statistics & Probability Letters, Elsevier, vol. 69(4), pages 381-388, October.
    2. Matsumoto, Hiroyuki & Wesolowski, Jacek & Witkowski, Piotr, 2009. "Tree structured independence for exponential Brownian functionals," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3798-3815, October.
    3. Wesolowski, Jacek & Witkowski, Piotr, 2007. "Hitting times of Brownian motion and the Matsumoto-Yor property on trees," Stochastic Processes and their Applications, Elsevier, vol. 117(9), pages 1303-1315, September.
    4. Bobecka, Konstancja, 2015. "The Matsumoto–Yor property on trees for matrix variates of different dimensions," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 22-34.
    5. Massam, Hélène & Wesolowski, Jacek, 2006. "The Matsumoto-Yor property and the structure of the Wishart distribution," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 103-123, January.
    6. Matsumoto, Hiroyuki & Yor, Marc, 2003. "Interpretation via Brownian motion of some independence properties between GIG and gamma variables," Statistics & Probability Letters, Elsevier, vol. 61(3), pages 253-259, February.
    7. Koudou, Angelo Efoévi, 2006. "A link between the Matsumoto-Yor property and an independence property on trees," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1097-1101, June.
    8. Koudou, Angelo Efoevi, 2012. "A Matsumoto–Yor property for Kummer and Wishart random matrices," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1903-1907.
    9. Stirzaker, David, 2005. "Stochastic Processes and Models," OUP Catalogue, Oxford University Press, number 9780198568148, Decembrie.
    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. Piliszek, Agnieszka & Wesołowski, Jacek, 2016. "Kummer and gamma laws through independences on trees—Another parallel with the Matsumoto–Yor property," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 15-27.
    2. Matsumoto, Hiroyuki & Wesolowski, Jacek & Witkowski, Piotr, 2009. "Tree structured independence for exponential Brownian functionals," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3798-3815, October.
    3. Wesolowski, Jacek & Witkowski, Piotr, 2007. "Hitting times of Brownian motion and the Matsumoto-Yor property on trees," Stochastic Processes and their Applications, Elsevier, vol. 117(9), pages 1303-1315, September.
    4. Bobecka, Konstancja, 2015. "The Matsumoto–Yor property on trees for matrix variates of different dimensions," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 22-34.
    5. Bartosz Kołodziejek, 2017. "The Matsumoto–Yor Property and Its Converse on Symmetric Cones," Journal of Theoretical Probability, Springer, vol. 30(2), pages 624-638, June.
    6. Letac, Gérard & Wesołowski, Jacek, 2020. "Multivariate reciprocal inverse Gaussian distributions from the Sabot–Tarrès–Zeng integral," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    7. Julien Chevallier & Benoît Sévi, 2014. "On the Stochastic Properties of Carbon Futures Prices," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 58(1), pages 127-153, May.
    8. Lee, Julian, 2023. "Poisson distributions in stochastic dynamics of gene expression: What events do they count?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    9. Chou, Chao-Wei & Huang, Wen-Jang, 2004. "On characterizations of the gamma and generalized inverse Gaussian distributions," Statistics & Probability Letters, Elsevier, vol. 69(4), pages 381-388, October.
    10. V. Seshadri & J. Wesołowski, 2008. "More on connections between Wishart and matrix GIG distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(2), pages 219-232, September.
    11. Hamza, Marwa & Vallois, Pierre, 2016. "On Kummer’s distribution of type two and a generalized beta distribution," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 60-69.
    12. Kawar Badie Mahmood & Adil Sufian Husain, 2021. "Bernoulli’s Number One Solution for Stochastic Equilibrium," International Journal of Science and Business, IJSAB International, vol. 5(8), pages 194-201.
    13. Koulovatianos, Christos & Wieland, Volker, 2011. "Asset pricing under rational learning about rare disasters," IMFS Working Paper Series 46, Goethe University Frankfurt, Institute for Monetary and Financial Stability (IMFS).
    14. Hariya, Yuu & Yor, Marc, 2004. "On an extension of Dufresne's relation between exponential Brownian functionals from opposite drifts to two different drifts: a short proof," Statistics & Probability Letters, Elsevier, vol. 67(4), pages 331-341, May.
    15. Burrell, Quentin L., 2007. "On the h-index, the size of the Hirsch core and Jin's A-index," Journal of Informetrics, Elsevier, vol. 1(2), pages 170-177.
    16. Burrell, Quentin L., 2007. "Hirsch's h-index: A stochastic model," Journal of Informetrics, Elsevier, vol. 1(1), pages 16-25.
    17. Bodnar, Taras & Mazur, Stepan & Okhrin, Yarema, 2013. "On the exact and approximate distributions of the product of a Wishart matrix with a normal vector," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 70-81.
    18. Tounsi, Mariem & Zine, Raoudha, 2012. "The inverse Riesz probability distribution on symmetric matrices," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 174-182.
    19. Jean-Marc Luck, 2019. "Parrondo games as disordered systems," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 92(8), pages 1-17, August.
    20. Robert Mill & Martin Coath & Thomas Wennekers & Susan L Denham, 2011. "A Neurocomputational Model of Stimulus-Specific Adaptation to Oddball and Markov Sequences," PLOS Computational Biology, Public Library of Science, vol. 7(8), pages 1-15, August.

    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:107:y:2015:i:c:p:145-149. 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.