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Discrete Tempered Stable Distributions

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  • Michael Grabchak

    (University of North Carolina Charlotte)

Abstract

Discrete tempered stable distributions are a large and flexible class of models for heavy tailed and overdispersed count data. In this paper we derive various properties of these distributions and develop an exact simulation method based on rejection sampling and a compound Poisson representation. We extend this method to exact simulation of the corresponding bilateral distributions and Lévy processes.

Suggested Citation

  • Michael Grabchak, 2022. "Discrete Tempered Stable Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1877-1890, September.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:3:d:10.1007_s11009-021-09904-3
    DOI: 10.1007/s11009-021-09904-3
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    References listed on IDEAS

    as
    1. Christoph, Gerd & Schreiber, Karina, 1998. "Discrete stable random variables," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 243-247, March.
    2. Zhu, Rong & Joe, Harry, 2009. "Modelling heavy-tailed count data using a generalised Poisson-inverse Gaussian family," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1695-1703, August.
    3. Klebanov, Lev B. & Slámová, Lenka, 2013. "Integer valued stable random variables," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1513-1519.
    4. Vincent Goulet & Christophe Dutang & Mathieu Pigeon, 2008. "actuar : An R Package for Actuarial Science," Post-Print hal-01616144, HAL.
    5. Shin Kim, Young & Rachev, Svetlozar T. & Leonardo Bianchi, Michele & Fabozzi, Frank J., 2010. "Tempered stable and tempered infinitely divisible GARCH models," Journal of Banking & Finance, Elsevier, vol. 34(9), pages 2096-2109, September.
    6. Grabchak, Michael, 2021. "An exact method for simulating rapidly decreasing tempered stable distributions in the finite variation case," Statistics & Probability Letters, Elsevier, vol. 170(C).
    7. Dutang, Christophe & Goulet, Vincent & Pigeon, Mathieu, 2008. "actuar: An R Package for Actuarial Science," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 25(i07).
    8. Ole E. Barndorff-Nielsen & David G. Pollard & Neil Shephard, 2012. "Integer-valued L�vy processes and low latency financial econometrics," Quantitative Finance, Taylor & Francis Journals, vol. 12(4), pages 587-605, January.
    9. Devroye, Luc, 1993. "A triptych of discrete distributions related to the stable law," Statistics & Probability Letters, Elsevier, vol. 18(5), pages 349-351, December.
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