IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v66y2014i5p833-864.html
   My bibliography  Save this article

Prediction in Ewens–Pitman sampling formula and random samples from number partitions

Author

Listed:
  • Masaaki Sibuya

Abstract

Motivated by marine ecological data on species abundance, with the record of subsamples, two problems are investigated in this paper, assuming the Ewens–Pitman sampling formula: One is the prediction of the number of new species if the catch is continued, and the other is how the number of species will decrease in random subsamples. Related statistics and extended models are also considered. A tool for the work is the generalized Stirling numbers of three variables. Copyright The Institute of Statistical Mathematics, Tokyo 2014

Suggested Citation

  • Masaaki Sibuya, 2014. "Prediction in Ewens–Pitman sampling formula and random samples from number partitions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(5), pages 833-864, October.
    • Handle: RePEc:spr:aistmt:v:66:y:2014:i:5:p:833-864
    DOI: 10.1007/s10463-013-0427-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10463-013-0427-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10463-013-0427-8?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. Lijoi, Antonio & Mena, Ramses H. & Prunster, Igor, 2005. "Hierarchical Mixture Modeling With Normalized Inverse-Gaussian Priors," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1278-1291, December.
    2. Masaaki Sibuya, 1993. "A random clustering process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(3), pages 459-465, September.
    3. Antonio Lijoi & Igor Pruenster & Stephen G. Walker, 2008. "Bayesian nonparametric estimators derived from conditional Gibbs structures," ICER Working Papers - Applied Mathematics Series 06-2008, ICER - International Centre for Economic Research.
    4. Nobuaki Hoshino, 2012. "Random partitioning over a sparse contingency table," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(3), pages 457-474, June.
    5. Charalambos A. Charalambides, 2007. "Distributions of Random Partitions and Their Applications," Methodology and Computing in Applied Probability, Springer, vol. 9(2), pages 163-193, June.
    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. Antonio Lijoi & Igor Pruenster, 2009. "Models beyond the Dirichlet process," ICER Working Papers - Applied Mathematics Series 23-2009, ICER - International Centre for Economic Research.
    2. Antonio Lijoi & Igor Prunster, 2009. "Models beyond the Dirichlet process," Quaderni di Dipartimento 103, University of Pavia, Department of Economics and Quantitative Methods.
    3. Shuhei Mano, 2017. "Extreme sizes in Gibbs-type exchangeable random partitions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 1-37, February.
    4. Stefano Favaro & Antonio Lijoi & Igor Prünster, 2012. "A new estimator of the discovery probability," DEM Working Papers Series 007, University of Pavia, Department of Economics and Management.
    5. Nobuaki Hoshino, 2012. "Random partitioning over a sparse contingency table," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(3), pages 457-474, June.
    6. Pierpaolo De Blasi & Stefano Favaro & Antonio Lijoi & Ramsés H. Mena & Igor Prünster & Mattteo Ruggiero, 2013. "Are Gibbs-type priors the most natural generalization of the Dirichlet process?," DEM Working Papers Series 054, University of Pavia, Department of Economics and Management.
    7. Kolossiatis, M. & Griffin, J.E. & Steel, M.F.J., 2011. "Modeling overdispersion with the normalized tempered stable distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2288-2301, July.
    8. Stefano Favaro & Antonio Lijoi & Igor Prünster, 2012. "On the stick–breaking representation of normalized inverse Gaussian priors," DEM Working Papers Series 008, University of Pavia, Department of Economics and Management.
    9. Sibuya, Masaaki & Yamato, Hajime, 1995. "Ordered and unordered random partitions of an integer and the GEM distribution," Statistics & Probability Letters, Elsevier, vol. 25(2), pages 177-183, November.
    10. Antonio Canale & Igor Prünster, 2017. "Robustifying Bayesian nonparametric mixtures for count data," Biometrics, The International Biometric Society, vol. 73(1), pages 174-184, March.
    11. Antonio Lijoi & Igor Pruenster, 2009. "Distributional Properties of means of Random Probability Measures," ICER Working Papers - Applied Mathematics Series 22-2009, ICER - International Centre for Economic Research.
    12. Canale, Antonio & Lijoi, Antonio & Nipoti, Bernardo & Prünster, Igor, 2023. "Inner spike and slab Bayesian nonparametric models," Econometrics and Statistics, Elsevier, vol. 27(C), pages 120-135.
    13. Antonio Canale & Bruno Scarpa, 2016. "Bayesian nonparametric location–scale–shape mixtures," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 113-130, March.
    14. Mena, Ramsés H. & Walker, Stephen G., 2012. "An EPPF from independent sequences of geometric random variables," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1059-1066.
    15. Martínez-Ovando Juan Carlos & Olivares-Guzmán Sergio I. & Roldán-Rodríguez Adriana, 2014. "Predictive Inference on Finite Populations Segmented in Planned and Unplanned Domains," Working Papers 2014-04, Banco de México.
    16. Stefano Favaro & Shui Feng & Fuqing Gao, 2018. "Moderate Deviations for Ewens-Pitman Sampling Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 330-341, August.
    17. Stefano Favaro & Antonio Lijoi & Ramsés H. Mena & Igor Prünster, 2009. "Bayesian non‐parametric inference for species variety with a two‐parameter Poisson–Dirichlet process prior," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 993-1008, November.
    18. Matteo Ruggiero & Matteo Sordello, 2018. "Clustering dynamics in a class of normalised generalised gamma dependent priors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(1), pages 83-98, February.
    19. Raffaele Argiento & Alessandra Guglielmi & Antonio Pievatolo, 2014. "Estimation, prediction and interpretation of NGG random effects models: an application to Kevlar fibre failure times," Statistical Papers, Springer, vol. 55(3), pages 805-826, August.
    20. Argiento, Raffaele & Guglielmi, Alessandra & Pievatolo, Antonio, 2010. "Bayesian density estimation and model selection using nonparametric hierarchical mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 816-832, April.

    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:spr:aistmt:v:66:y:2014:i:5:p:833-864. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.