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A triptych of discrete distributions related to the stable law


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  • Devroye, Luc
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    We derive useful distributional representations for three discrete laws: the discrete stable distribution of Steutel and Van Harn, the discrete Linnik distribution introduced by Pakes, and a distribution of Sibuya. These representations may be used to obtain simple uniformly fast random variate generators.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 18 (1993)
    Issue (Month): 5 (December)
    Pages: 349-351

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    Handle: RePEc:eee:stapro:v:18:y:1993:i:5:p:349-351

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    Keywords: Discrete stable distribution random variate generation distribution theory Linnik's distribution;


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    Cited by:
    1. Rodrigues, Josemar & Balakrishnan, N. & Cordeiro, Gauss M. & de Castro, Mário, 2011. "A unified view on lifetime distributions arising from selection mechanisms," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3311-3319, December.
    2. Christoph, Gerd & Schreiber, Karina, 1998. "Discrete stable random variables," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 243-247, March.
    3. Orsingher, Enzo & Polito, Federico, 2012. "The space-fractional Poisson process," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 852-858.
    4. Weron, Rafal, 1996. "On the Chambers-Mallows-Stuck method for simulating skewed stable random variables," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 165-171, June.
    5. Emad-Eldin Aly & Nadjib Bouzar, 2002. "A Notion of α-Monotonicity with Generalized Multiplications," Annals of the Institute of Statistical Mathematics, Springer, vol. 54(1), pages 125-137, March.
    6. Sapatinas, Theofanis, 1995. "Characterizations of probability distributions based on discrete p-monotonicity," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 339-344, September.
    7. Aoki, Masanao, 2008. "Thermodynamic limits of macroeconomic or financial models: One- and two-parameter Poisson-Dirichlet models," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 66-84, January.
    8. Kotz, Samuel & Ostrovskii, I. V., 1996. "A mixture representation of the Linnik distribution," Statistics & Probability Letters, Elsevier, vol. 26(1), pages 61-64, January.
    9. Christoph, Gerd & Schreiber, Karina, 2000. "Scaled Sibuya distribution and discrete self-decomposability," Statistics & Probability Letters, Elsevier, vol. 48(2), pages 181-187, June.
    10. Soltani, A.R. & Shirvani, A. & Alqallaf, F., 2009. "A class of discrete distributions induced by stable laws," Statistics & Probability Letters, Elsevier, vol. 79(14), pages 1608-1614, July.
    11. Masanao Aoki, 2006. "Thermodynamic Limits of Macroeconomic or Financial Models: One-and Two-Parameter Poisson-Dirichlet Models (Forthcoming in "Journal of Economic Dynamics and Control", 2007. )," CARF F-Series CARF-F-083, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    12. 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.
    13. AOKI Masanao & YOSHIKAWA Hiroshi, 2007. "Non-Self-Averaging in Macroeconomic Models: A Criticism of Modern Micro-founded Macroeconomics," Discussion papers 07057, Research Institute of Economy, Trade and Industry (RIETI).
    14. Nadjib Bouzar, 2008. "The semi-Sibuya distribution," Annals of the Institute of Statistical Mathematics, Springer, vol. 60(2), pages 459-464, June.
    15. Masanao Aoki & Hiroshi Yoshikawa, 2007. "Non-Self-Averaging in Macroeconomic Models: A Criticism of Modern Micro-founded Macroeconomics," CIRJE F-Series CIRJE-F-493, CIRJE, Faculty of Economics, University of Tokyo.


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