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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

  • Brix A (1999) Generalized gamma measures and shot-noise Cox processes. Adv Appl Probab 31:929–953

    Article  MATH  MathSciNet  Google Scholar 

  • Cifarelli DM, Regazzini E (1979) A general approach to Bayesian analysis of nonparametric problems. The associative mean values within the framework of the Dirichlet process. II. (Italian) Riv. Math Sci Econ Soc 2:95–111

    MATH  MathSciNet  Google Scholar 

  • Cifarelli DM, Regazzini E (1990) Distribution functions of means of a Dirichlet process. Ann Stat 18: 429–442

  • Cont R, Tankov P (2004) Financial modelling with jump processes. Chapman and Hall, Boca Raton

    MATH  Google Scholar 

  • De Blasi P, Favaro S, Lijoi A, Mena R, Prünster I, Ruggiero M (2014) Are Gibbs-type priors the most natural generalization of the Dirichlet process? Pattern Anal Mach Intell, IEEE Trans. doi:10.1109/TPAMI.2013.217

  • Diaconis P, Kemperman J (1996) Some new tools on Dirichlet priors. In: Bernardo JM, Berger JO, Dawid AP, Smith AFM (eds) Bayesian statistics, vol 5. Oxford University Press, New York, pp 97–106

    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 

  • Devroye L, James LF (2011) The double CFTP method. ACM Trans Model Comput Simul 21:1–20

    Article  Google Scholar 

  • Ferguson TS (1973) A Bayesian analysis of some nonparametric problems. Ann Stat 1:209–230

    Article  MATH  MathSciNet  Google Scholar 

  • Ferguson TS, Klass MJ (1972) A representation of independent increment processes without Gaussian components. Ann Math Stat 43:1634–1643

    Article  MATH  MathSciNet  Google Scholar 

  • Griffiths RC, Milne RK (1978) A class of bivariate Poisson processes. J Mult Anal 8:380–395

    Article  MATH  MathSciNet  Google Scholar 

  • Guglielmi A, Holmes CC, Walker SG (2002) Perfect simulation involving functionals of a Dirichlet process. J Comput Graph Stat 11:306–310

    Article  MathSciNet  Google Scholar 

  • Ishwaran H, James LF (2001) Gibbs sampling methods for stick-breaking priors. J Am Stat Assoc 96:161–173

    Article  MATH  MathSciNet  Google Scholar 

  • Ishwaran H, Zarepour M (2009) Series representations for multivariate generalized gamma processes via a scale invariance principle. Stat Sinica 19:1665–1682

    MATH  MathSciNet  Google Scholar 

  • James LF (2006) Functionals of Dirichlet processes, the Cifarelli-Regazzini identity and beta-gamma processes. Ann Stat 33:647–660

    Article  Google Scholar 

  • James LF, Lijoi A, Prünster I (2009) Posterior analysis for normalized random measures with independent increments. Scand J Stat 36:76–97

    Article  MATH  MathSciNet  Google Scholar 

  • James LF, Lijoi A, Prünster I (2010) On the posterior distribution of classes of random means. Bernoulli 16:155–180

    Article  MATH  MathSciNet  Google Scholar 

  • Lijoi A, Nipoti B, Prünster I (2014a) Bayesian inference with dependent normalized completely random measures. Bernoulli. doi:10.3150/13-BEJ521

  • Lijoi A, Nipoti B, Prünster I (2014b) Dependent mixture models: clustering and borrowing information. Comput Stat Data Anal 71:417–433

    Article  Google Scholar 

  • Lijoi A, Prünster I (2009) Distributional properties of means of random probability measures. Stat Surv 3:47–95

    Article  MATH  MathSciNet  Google Scholar 

  • Lijoi A, Prünster I (2010) Models beyond the Dirichlet process. In: Hjort NL, Holmes CC, Müller P, Walker SG (eds) Bayesian nonparametrics. Cambridge University Press, Cambridge, pp 80–136

    Chapter  Google Scholar 

  • Perman M, Pitman J, Yor M (1992) Size-biased sampling of Poisson point processes and excursions. Probab Theory Relat Fields 92:21–39

    Article  MATH  MathSciNet  Google Scholar 

  • Pitman, J. (1996). Some developments of the Blackwell-MacQueen urn scheme. In: Ferguson TS, Shapley LS, MacQueen JB (eds) Statistics, probability and game theory IMS lecture notes monograph series vol 30, Inst Math Statist. Hayward, pp 245–267

  • Walker SG (2007) Sampling the Dirichlet mixture model with slices. Commun Stat Simul Comput 36:45–54

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Economics and Management, University of Pavia, Pavia, Italy

    Antonio Lijoi

  2. Department of Economics and Statistics, University of Torino, Turin, Italy

    Igor Prünster

Authors
  1. Antonio Lijoi
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  2. Igor Prünster
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Corresponding author

Correspondence to Antonio Lijoi.

Additional information

A. Lijoi and I. Prünster are also affiliated to Collegio Carlo Alberto, Moncalieri, Italy. Support from the European Research Council (ERC) through StG “N-BNP” 306406 is gratefully acknowledged.

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Lijoi, A., Prünster, I. Discussion of “On simulation and properties of the stable law” by L. Devroye and L. James. Stat Methods Appl 23, 371–377 (2014). https://doi.org/10.1007/s10260-014-0269-4

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  • DOI: https://doi.org/10.1007/s10260-014-0269-4

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