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

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  • 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

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  • 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
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    References listed on IDEAS

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    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.
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