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Discussion of “On simulation and properties of the stable law” by L. Devroye and L. James

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References

  • Barabesi L, Pratelli L (2014a) A note on a universal random variate generator for integer-valued random variables. Stat Comput (in press)

  • Barabesi L, Pratelli L (2014b) Universal methods for generating random variables with a given characteristic function. J Stat Comput Simul (in press)

  • Christoph G, Schreiber K (2001) Positive Linnik and discrete Linnik distributions. In: Balakrishnan N, Ibragimov IA, Nevzorov VB (eds) Asymptotic methods in probability and statistics with applications. Birkhäuser, Boston, pp 3–17

    Chapter  Google Scholar 

  • Devroye L (1992) Random variate generation for the digamma and trigamma distributions. J Stat Comput Simul 43:197–216

    Article  MathSciNet  Google Scholar 

  • Devroye L (1993) A triptych of discrete distribution related to the stable law. Stat Probab Lett 18:349–351

    Article  MATH  MathSciNet  Google Scholar 

  • Devroye L (2009) Random variate generation for exponentially and polynomially tilted stable distributions. ACM Trans Model Comput Simul 19:18

    Article  Google Scholar 

  • Doray LG, Jiang SM, Luong A (2009) Some simple method of estimation for the parameters of the discrete stable distribution with the probability generating function. Commun Stat Simul Comput 38:2004–2017

    Article  MATH  MathSciNet  Google Scholar 

  • El-Shaarawi AH, Zhu R, Joe H (2009) Modelling species abundance using the Poisson–Tweedie family. Environmetrics 22:152–164

    Article  MathSciNet  Google Scholar 

  • Hofert M (2011) Sampling exponentially tilted stable distributions. ACM Trans Model Comput Simul 22:3

    Article  MathSciNet  Google Scholar 

  • Kanter M (1975) Stable densities under change of scale and total variation inequalities. Ann Probab 3:697–707

    Article  MATH  MathSciNet  Google Scholar 

  • Klebanov LB, Slámová L (2013) Integer valued stable random variables. Stat Probab Lett 83:1513–1519

    Article  MATH  Google Scholar 

  • Marcheselli M, Baccini A, Barabesi L (2008) Parameter estimation for the discrete stable family. Commun Stat Theory Methods 37:815–830

    Article  MATH  MathSciNet  Google Scholar 

  • Pakes AG (1995) Characterization of discrete stable laws via mixed sums and Markov branching processes. Stoch Process Their Appl 55:285–300

    Article  MATH  MathSciNet  Google Scholar 

  • Pillai RN, Jayakumar K (1995) Discrete Mittag-Leffler distributions. Stat Probab Lett 23:271–274

    Article  MATH  MathSciNet  Google Scholar 

  • Slámová L, Klebanov LB (2012) Modeling financial returns by discrete stable distributions. In: Ramík J, Stavárek D (eds) Proceedings of the 30th International Conference Mathematical Methods in Economics 2012. Silesian University in Opava, School of Business Administration in Karviná, pp 805–810

  • Sato K (1999) Lévy processes and infinitely divisible distributions. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Steutel FW, van Harn K (1979) Discrete analogues of self-decomposability and stability. Ann Probab 7:893–899

    Article  MATH  MathSciNet  Google Scholar 

  • Steutel FW, van Harn K (2004) Infinite divisibility of probability distributions on the real line. Dekker, New York

    MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. Dipartimento di Economia Politica e Statistica, Università di Siena, P.zza S.Francesco 7, 53100 , Siena, Italy

    Lucio Barabesi

  2. Gruppo Matematiche, Accademia Navale, Viale Italia 72, 57121 , Leghorn, Italy

    Luca Pratelli

Authors
  1. Lucio Barabesi
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  2. Luca Pratelli
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Correspondence to Lucio Barabesi.

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Barabesi, L., Pratelli, L. Discussion of “On simulation and properties of the stable law” by L. Devroye and L. James. Stat Methods Appl 23, 345–351 (2014). https://doi.org/10.1007/s10260-014-0263-x

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  • DOI: https://doi.org/10.1007/s10260-014-0263-x

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