Abstract.
A brief survey of work done on two long-standing and important problems in statistics is given. In a simple random sample (with replacement) of size n from a population divided into species, if N distinct species are observed, what is the probability that, on the next trial, a species not observed before is discovered? And what is the total number of species not observed? Interesting in many applied areas, these problems have been discussed in a great number of papers. We survey some of the related publications as well as a Bayes-like estimator recently devised by the authors, together with results on the estimation of the distribution of the probability of discovering a new species.
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Dedicated to the memory of Bruno Forte, mentor and friend to one of us
Lecture held by C.C.A. Sastri in the Seminario Matematico e Fisico on May 12, 2003
Received: June, 2004
An erratum to this article is available at http://dx.doi.org/10.1007/s00032-005-0049-6.
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Gandolfi, A., Sastri, C.C.A. Nonparametric Estimations about Species Not Observed in a Random Sample. Milan j. math. 72, 81–105 (2004). https://doi.org/10.1007/s00032-004-0031-8
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DOI: https://doi.org/10.1007/s00032-004-0031-8